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Create the page "M(1,1,1)" on this wiki! See also the search results found.

Page title matches

• M(16,10,1)
  |title = M(16,10,1) - <math>k(C_4 \times C_2 \times C_2)</math> |inertialquotients = <math>1</math>
  2 KB (256 words) - 09:41, 4 December 2018
• M(3,1,1)
  |title = M(3,1,1) - <math>kC_3</math> |image = M(2,1,1)quiver.png
  2 KB (225 words) - 15:59, 7 October 2018
• M(3,1,2)
  |title = M(3,1,2) - <math>kS_3</math> |image = M(3,1,2)quiver.png
  2 KB (279 words) - 22:30, 9 September 2018
• M(2,1,1)
  |title = M(2,1,1) - <math>kC_2</math> |image =M(2,1,1)quiver.png
  2 KB (230 words) - 13:18, 9 September 2018
• M(4,1,1)
  |title = M(4,1,1) - <math>kC_4</math> |image = M(2,1,1)quiver.png
  2 KB (211 words) - 13:23, 9 September 2018
• M(4,2,1)
  |title = M(4,2,1) - <math>k(C_2 \times C_2)</math> |image = M(4,2,1)quiver.png
  2 KB (253 words) - 14:30, 19 December 2018
• M(5,1,1)
  |title = M(5,1,1) - <math>kC_5</math> |image = M(2,1,1)quiver.png
  1 KB (177 words) - 23:44, 2 January 2019
• M(25,1,1)
  |title = M(25,1,1) - <math>kC_{25}</math> |image = M(2,1,1)quiver.png
  2 KB (269 words) - 16:24, 8 October 2018
• M(5,1,2)
  |title = M(5,1,2) - <math>kD_{10}</math> |image = M(5,1,2)quiver.png
  2 KB (245 words) - 10:32, 4 September 2018
• M(5,1,3)
  |title = M(5,1,3) - <math>B_0(kA_5)</math> |image = M(5,1,3)quiver.png
  2 KB (252 words) - 10:31, 4 September 2018
• M(5,1,4)
  |title = M(5,1,4) - <math>k(C_5:C_4)</math> |image = M(5,1,4)quiver.png
  2 KB (290 words) - 10:33, 4 September 2018
• M(5,1,5)
  |title = M(5,1,5) - <math>B_0(kA_7)</math> |image = M(5,1,5)quiver.png
  2 KB (288 words) - 10:20, 4 September 2018
• M(5,1,6)
  |title = M(5,1,6) - <math>B_{15}(k(6.A_7))</math> |image = M(5,1,6)quiver.png
  2 KB (202 words) - 08:56, 28 September 2018
• M(9,1,1)
  |title = M(9,1,1) - <math>kC_9</math> |image = M(2,1,1)quiver.png
  1 KB (163 words) - 17:56, 1 February 2019
• M(9,1,2)
  |title = M(9,1,2) - <math>kD_{18}</math> |image = M(5,1,2)quiver.png
  2 KB (265 words) - 21:43, 5 September 2018
• M(9,1,3)
  |title = M(9,1,3) - <math>B_0(kPSL_2(8))</math> |image = M(5,1,3)quiver.png
  2 KB (267 words) - 21:56, 5 September 2018
• M(27,1,1)
  |title = M(27,1,1) - <math>kC_{27}</math> |image = M(2,1,1)quiver.png
  2 KB (254 words) - 13:30, 9 September 2018
• M(27,1,2)
  |title = M(27,1,2) - <math>kD_{54}</math> |image = M(5,1,2)quiver.png
  2 KB (265 words) - 17:49, 6 September 2018
• M(27,1,3)
  |title = M(27,1,3) - <math>B_0(kPSL_2(53))</math> |image = M(5,1,3)quiver.png
  2 KB (270 words) - 17:54, 6 September 2018
• M(3^n,1,1)
  |title = M(3^n,1,1) - <math>kC_{3^n}</math> |image = M(2,1,1)quiver.png
  2 KB (225 words) - 08:44, 3 December 2018
• M(3^n,1,2)
  |title = M(3^n,1,2) - <math>kD_{2.3^n}</math> |image = M(5,1,2)quiver.png
  2 KB (290 words) - 15:22, 8 September 2018
• M(3^n,1,3)
  |title = M(3^n,1,3) - <math>B_0(kPSL_2(2^{(3^{n-1})}))</math> |image = M(5,1,3)quiver.png
  2 KB (310 words) - 15:40, 8 September 2018
• M(8,1,1)
  |title = M(8,1,1) - <math>kC_8</math> |image = M(2,1,1)quiver.png
  2 KB (233 words) - 15:16, 7 October 2018
• M(2^n,1,1)
  |title = M(2^n,1,1) - <math>kC_{2^n}</math> |inertialquotients = <math>1</math>
  2 KB (240 words) - 16:03, 8 September 2018
• M(8,2,1)
  |title = M(8,2,1) - <math>k(C_4 \times C_2)</math> |image = M(4,2,1)quiver.png
  2 KB (187 words) - 12:33, 1 November 2018
• M(8,5,1)
  |title = M(8,5,1) - <math>k(C_2 \times C_2 \times C_2)</math> |inertialquotients = <math>1</math>
  2 KB (263 words) - 14:25, 27 November 2019
• M(8,3,1)
  |title = M(8,3,1) - <math>kD_8</math> |image = M(4,2,1)quiver.png
  1 KB (153 words) - 22:47, 5 October 2018
• M(16,2,1)
  |title = M(16,2,1) - <math>k(C_4 \times C_4)</math> |image = M(4,2,1)quiver.png
  1 KB (165 words) - 13:00, 15 November 2018
• M(16,1,1)
  |title = M(16,1,1) - <math>kC_{16}</math> |image = M(2,1,1)quiver.png
  1 KB (172 words) - 15:22, 7 October 2018
• M(8,4,1)
  |title = M(8,4,1) - <math>kQ_8</math> |image = M(4,2,1)quiver.png
  1 KB (158 words) - 09:36, 24 May 2022
• M(9,2,1)
  |title = M(9,2,1) - <math>k(C_3 \times C_3)</math> |image = M(4,2,1)quiver.png
  2 KB (185 words) - 18:16, 21 October 2018
• M(16,14,1)
  |title = M(16,14,1) - <math>k((C_2)^4)</math> |inertialquotients = <math>1</math>
  2 KB (226 words) - 15:42, 28 November 2019
• M(32,51,1)
  |title = M(32,51,1) - <math>k((C_2)^5)</math> |inertialquotients = <math>1</math>
  2 KB (245 words) - 15:17, 5 December 2019

Page text matches

• Statements of conjectures
  ...>V, W</math> of simple <math>B</math>-modules, <math>\dim_k({\rm Ext}_{kG}^1(V,W)) \leq e</math> ...defect groups isomorphic to <math>P</math>, then <math>{\rm mf}_k(B) \leq m</math>.
  6 KB (970 words) - 16:15, 21 August 2020
• C2
  ...|| 1 ||2 ||1 ||<math>1</math> ||<math>C_2</math> ||<math>k^*</math> ||1 ||1 ||
  868 bytes (126 words) - 22:59, 21 November 2018
• C3
  ...1</math> ||<math>S_3</math> || <math>k:k^*</math> ||1 ||1 || [[Image:M(3,1,1)tree.png|45px]] ...> ||<math>C_2</math> || <math>k^* \times C_2</math> ||1 ||1 || [[Image:M(3,1,2)tree.png|45px]]
  1 KB (154 words) - 11:20, 22 November 2018
• C4
  ...<math>D_8</math> || <math>(k \times k):k^*</math> ||1 ||1 || [[Image:M(4,1,1)tree.png|45px]]
  880 bytes (129 words) - 11:18, 22 November 2018
• C9
  ...||1 ||<math>1</math> ||<math>C_9 : C_6</math> || ||1 ||1 || [[Image:M(9,1,1)tree.png|45px]] ...<math>C_2</math> || <math>C_2 \times C_3</math> || ||1 ||1 || [[Image:M(9,1,2)tree.png|45px]]
  1 KB (168 words) - 11:27, 22 November 2018
• References
  ...[[#F|F,]] [[#G|G,]] [[#H|H,]] [[#I|I,]] [[#J|J,]] [[#K|K,]] [[#L|L,]] [[#M|M,]] [[#N|N,]] [[#O|O,]] [[#P|P,]] [[#Q|Q,]] [[#R|R,]] [[#S|S,]] [[#T|T]] [[# ...and Quillen's dimension theorem'', J. Pure Appl. Algebra '''22''' (1981), 1-9.
  21 KB (2,957 words) - 12:29, 2 May 2024
• C2xC2
  ...ath>(C_2 \times C_2):S_3</math> || <math>(k \times k):GL_2(k)</math> ||1 ||1 || ...h>C_3</math> ||<math>C_2</math> || <math>(k^* \times k^*):C_2</math> ||1 ||1 || <math>D(3 {\cal A})_1</math>
  1 KB (218 words) - 09:04, 15 September 2018
• C5
  ...|5 ||1 ||<math>1</math> ||<math>C_5:C_4</math> || ||1 ||1 || [[Image:M(5,1,1)tree.png|45px]] ...|<math>C_2</math> || <math>C_2 \times C_2</math> || ||1 ||1 || [[Image:M(5,1,2)tree.png|45px]]
  1 KB (205 words) - 11:28, 22 November 2018
• C8
  ...1</math> ||<math>C_8:(C_2 \times C_2)</math> || <math>k^6:k^*</math> ||1 ||1 ||
  857 bytes (125 words) - 11:19, 22 November 2018
• C25
  ...</math> ||25 ||1 || <math>1</math> ||<math>C_{25} : C_{20}</math> || ||1 ||1 || ...h> ||14 ||2 || <math>C_2</math> || <math>C_2 \times C_{10}</math> || ||1 ||1 ||
  2 KB (229 words) - 11:31, 22 November 2018
• C4xC2
  ...ath> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 ||
  813 bytes (123 words) - 09:08, 15 September 2018
• D8
  |[[M(8,3,1)]] || <math>kD_8</math> || 1 ||5 ||1 ||<math>1</math> || || || ||1 || ...]] || <math>B_0(kPGL_2(5))</math> || ? ||5 ||2 ||<math>1</math> || || || ||1 || <math>D(2 {\cal A})</math>
  2 KB (212 words) - 17:54, 18 December 2018
• Q8
  ...ath>kQ_8</math> || 1 ||5 ||1 ||<math>1</math> || <math>S_4</math> || ||1 ||1 || ...L_2(5))</math> || 1 ||7 ||3 ||<math>C_3</math> || <math>C_2</math> || || ||1 || <math>Q(3 {\cal A})_2</math>
  1 KB (184 words) - 09:35, 24 May 2022
• M(16,10,1)
  |title = M(16,10,1) - <math>k(C_4 \times C_2 \times C_2)</math> |inertialquotients = <math>1</math>
  2 KB (256 words) - 09:41, 4 December 2018
• M(3,1,1)
  |title = M(3,1,1) - <math>kC_3</math> |image = M(2,1,1)quiver.png
  2 KB (225 words) - 15:59, 7 October 2018
• M(3,1,2)
  |title = M(3,1,2) - <math>kS_3</math> |image = M(3,1,2)quiver.png
  2 KB (279 words) - 22:30, 9 September 2018
• M(2,1,1)
  |title = M(2,1,1) - <math>kC_2</math> |image =M(2,1,1)quiver.png
  2 KB (230 words) - 13:18, 9 September 2018
• M(4,1,1)
  |title = M(4,1,1) - <math>kC_4</math> |image = M(2,1,1)quiver.png
  2 KB (211 words) - 13:23, 9 September 2018
• M(4,2,1)
  |title = M(4,2,1) - <math>k(C_2 \times C_2)</math> |image = M(4,2,1)quiver.png
  2 KB (253 words) - 14:30, 19 December 2018
• M(4,2,2)
  |title = M(4,2,2) - <math>B_0(kA_5)</math> |image = M(4,2,2)quiver.png
  2 KB (309 words) - 15:47, 4 January 2019
• M(4,2,3)
  |title = M(4,2,3) - <math>kA_4</math> |image = M(4,2,3)quiver.png
  3 KB (348 words) - 16:29, 22 November 2018
• M(5,1,1)
  |title = M(5,1,1) - <math>kC_5</math> |image = M(2,1,1)quiver.png
  1 KB (177 words) - 23:44, 2 January 2019
• M(25,1,1)
  |title = M(25,1,1) - <math>kC_{25}</math> |image = M(2,1,1)quiver.png
  2 KB (269 words) - 16:24, 8 October 2018
• Generic classifications by p-group class
  Let <math>l,m,n,r \geq 2</math> be distinct. |[[C(2^n)|<math>C_{2^n}</math>]] || 1 || 1 || Yes || [[References#L|[Li96]]] || [[Blocks with cyclic defect groups]]
  11 KB (1,772 words) - 12:15, 9 January 2024
• C2xC2xC2
  ...math>1</math> || <math>(C_2 \times C_2 \times C_2):GL_3(2)</math> || ||1 ||1 || ...th> || 1 ||8 ||3 ||<math>C_3</math> || <math>C_2 \times C_2</math>|| ||1 ||1 ||
  2 KB (322 words) - 17:49, 23 September 2019
• M(5,1,2)
  |title = M(5,1,2) - <math>kD_{10}</math> |image = M(5,1,2)quiver.png
  2 KB (245 words) - 10:32, 4 September 2018
• M(5,1,3)
  |title = M(5,1,3) - <math>B_0(kA_5)</math> |image = M(5,1,3)quiver.png
  2 KB (252 words) - 10:31, 4 September 2018
• M(5,1,4)
  |title = M(5,1,4) - <math>k(C_5:C_4)</math> |image = M(5,1,4)quiver.png
  2 KB (290 words) - 10:33, 4 September 2018
• M(5,1,5)
  |title = M(5,1,5) - <math>B_0(kA_7)</math> |image = M(5,1,5)quiver.png
  2 KB (288 words) - 10:20, 4 September 2018
• M(5,1,6)
  |title = M(5,1,6) - <math>B_{15}(k(6.A_7))</math> |image = M(5,1,6)quiver.png
  2 KB (202 words) - 08:56, 28 September 2018
• C27
  ...}</math> ||27 ||1 ||<math>1</math> ||<math>C_{27} : C_{18}</math> || ||1 ||1 || ...kD_{54}</math> ||15 ||2 ||<math>C_2</math> || <math>C_{18}</math> || ||1 ||1 ||
  1 KB (148 words) - 11:26, 22 November 2018
• Glossary
  ...> with defect group <math>D</math> has height <math>h</math> if <math>\chi(1)_p=p^h[G:D]_p</math>. ...h>G</math> such that <math>B</math> covers a block <math>b</math> in <math>M</math> of <math>kN</math> for some normal subgroup <math>N</math> of <math>
  5 KB (841 words) - 23:02, 18 November 2020
• M(9,1,1)
  |title = M(9,1,1) - <math>kC_9</math> |image = M(2,1,1)quiver.png
  1 KB (163 words) - 17:56, 1 February 2019
• M(9,1,2)
  |title = M(9,1,2) - <math>kD_{18}</math> |image = M(5,1,2)quiver.png
  2 KB (265 words) - 21:43, 5 September 2018
• M(9,1,3)
  |title = M(9,1,3) - <math>B_0(kPSL_2(8))</math> |image = M(5,1,3)quiver.png
  2 KB (267 words) - 21:56, 5 September 2018
• M(27,1,1)
  |title = M(27,1,1) - <math>kC_{27}</math> |image = M(2,1,1)quiver.png
  2 KB (254 words) - 13:30, 9 September 2018
• M(27,1,2)
  |title = M(27,1,2) - <math>kD_{54}</math> |image = M(5,1,2)quiver.png
  2 KB (265 words) - 17:49, 6 September 2018
• M(27,1,3)
  |title = M(27,1,3) - <math>B_0(kPSL_2(53))</math> |image = M(5,1,3)quiver.png
  2 KB (270 words) - 17:54, 6 September 2018
• C(3^n)
  ...l the [[Glossary#Possible Brauer tree|possible Brauer trees]]. For <math>n=1</math> there are just two Morita equivalence classes (see [[C3|<math>C_3</m ...r such that <math>(q_n+1)_3=3^n</math>. For example take <math>q_n=2^{3^{n-1}}</math>.
  2 KB (257 words) - 23:34, 2 January 2019
• M(3^n,1,1)
  |title = M(3^n,1,1) - <math>kC_{3^n}</math> |image = M(2,1,1)quiver.png
  2 KB (225 words) - 08:44, 3 December 2018
• M(3^n,1,2)
  |title = M(3^n,1,2) - <math>kD_{2.3^n}</math> |image = M(5,1,2)quiver.png
  2 KB (290 words) - 15:22, 8 September 2018
• M(3^n,1,3)
  |title = M(3^n,1,3) - <math>B_0(kPSL_2(2^{(3^{n-1})}))</math> |image = M(5,1,3)quiver.png
  2 KB (310 words) - 15:40, 8 September 2018
• M(8,1,1)
  |title = M(8,1,1) - <math>kC_8</math> |image = M(2,1,1)quiver.png
  2 KB (233 words) - 15:16, 7 October 2018
• C(2^n)
  ...</math> ||1 ||<math>1</math> ||<math>C_{2^n} : C_{2^{n-1}}</math> || ||1 ||1 ||
  743 bytes (117 words) - 15:57, 8 September 2018
• M(2^n,1,1)
  |title = M(2^n,1,1) - <math>kC_{2^n}</math> |inertialquotients = <math>1</math>
  2 KB (240 words) - 16:03, 8 September 2018
• M(8,2,1)
  |title = M(8,2,1) - <math>k(C_4 \times C_2)</math> |image = M(4,2,1)quiver.png
  2 KB (187 words) - 12:33, 1 November 2018
• M(8,5,1)
  |title = M(8,5,1) - <math>k(C_2 \times C_2 \times C_2)</math> |inertialquotients = <math>1</math>
  2 KB (263 words) - 14:25, 27 November 2019
• M(8,5,3)
  |title = M(8,5,3) - <math>k(A_4 \times C_2)</math> |image = M(8,5,3)quiver.png
  3 KB (344 words) - 22:07, 5 December 2018
• Labelling for Morita equivalence classes
  M(x,y,z) is a class consisting of blocks with defect groups of order x, with ...ss of a defect group is a Morita invariant, so it could be that M(x,y1,z1)=M(x,y2,z2) for some <math>(y1,z1) \neq (y2,z2)</math>.
  3 KB (477 words) - 11:08, 3 October 2023
• C7
  ...7 ||1 ||<math>1</math> || <math>C_7:C_6</math> || ||1 ||1 || [[Image:M(7,1,1)tree.png|45px]] ...|<math>C_2</math> || <math>C_2 \times C_3</math> || ||1 ||1 || [[Image:M(7,1,2)tree.png|45px]]
  4 KB (465 words) - 12:58, 22 November 2018
• M(8,3,1)
  |title = M(8,3,1) - <math>kD_8</math> |image = M(4,2,1)quiver.png
  1 KB (153 words) - 22:47, 5 October 2018
• M(8,4,3)
  |title = M(8,4,3) - <math>kSL_2(3)</math> |image = M(4,2,3)quiver.png
  2 KB (290 words) - 15:51, 3 June 2021
• M(8,5,2)
  |title = M(8,5,2) - <math>B_0(k(A_5 \times C_2))</math> |image = M(8,5,2)quiver.png
  2 KB (326 words) - 21:49, 5 December 2018
• Blocks with basic algebras of low dimension
  | 1 || [[M(1,1,1)]] || <math>1</math> || <math>k1</math> || 1 || 1 || Blocks of defect zero | 2 || [[M(2,1,1)]] || <math>C_2</math> || <math>kC_2</math> || 2 || 1 ||
  4 KB (528 words) - 14:33, 13 December 2023
• M(8,5,4)
  |title = M(8,5,4) - <math>k((C_2 \times C_2 \times C_2):C_7)</math> |image = M(8,5,4)quiver.png
  4 KB (595 words) - 10:09, 5 June 2019
• M(8,5,5)
  |title = M(8,5,5) - <math>B_0(kSL_2(8))</math> |image = M(8,5,5)quiver.png
  3 KB (387 words) - 17:22, 21 November 2018
• M(8,3,4)
  |title = M(8,4,3) - <math>B_0(kPSL_2(9))</math> |image = M(4,2,2)quiver.png
  2 KB (218 words) - 17:51, 4 October 2018
• M(8,3,2)
  |title = M(8,3,2) - <math>B_0(kPGL_2(5))</math> |image = M(5,1,3)quiver.png
  2 KB (187 words) - 15:09, 4 October 2018
• M(8,3,3)
  |title = M(8,3,3) - <math>kS_4</math> |image = M(8,3,3)quiver.png
  2 KB (205 words) - 23:53, 18 December 2018
• M(8,5,7)
  |title = M(8,5,7) - <math>B_0(kJ_1)</math> |image = M(8,5,7)quiver.png
  3 KB (241 words) - 10:10, 5 June 2019
• C4xC2xC2
  ...times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)</math> || ||1 ||1 || ...> || 1 ||16 ||3 ||<math>C_3</math> || <math>D_8 \times C_2</math> || ||1 ||1 ||
  1 KB (177 words) - 15:01, 7 October 2019
• (C2)^4
  ...h> || 1 ||16 ||1 ||<math>1</math> || <math>(C_2)^4:GL_4(2)</math> || ||1 ||1 || ...math>C_3</math> || <math>((C_2 \times C_2):S_3) \times C_2</math> || ||1 ||1 ||
  4 KB (524 words) - 18:39, 9 December 2019
• C4xC4
  ...math> ||<math>(C_4 \times C_4):({\rm Aut}(C_4 \times C_4))</math> || ||1 ||1 || ...k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> || || ||1 ||1 ||
  1 KB (167 words) - 08:13, 4 June 2019
• M(16,2,1)
  |title = M(16,2,1) - <math>k(C_4 \times C_4)</math> |image = M(4,2,1)quiver.png
  1 KB (165 words) - 13:00, 15 November 2018
• M(16,2,2)
  |title = M(16,2,2) - <math>k((C_4 \times C_4):C_3)</math> |image = M(4,2,3)quiver.png
  2 KB (237 words) - 10:57, 28 July 2019
• M(8,3,6)
  |title = M(8,3,6) - <math>B_0(kPSL_2(7))</math> |image = M(4,2,3)quiver.png
  2 KB (232 words) - 21:48, 4 October 2018
• M(8,3,5)
  |title = M(8,3,5) - <math>B_0(kA_7)</math> |image = M(8,3,5)quiver.png
  2 KB (228 words) - 22:11, 4 October 2018
• C16
  ...h> ||<math>C_{16}:(C_4 \times C_2)</math> || <math>k^{14}:k^*</math> ||1 ||1 ||
  871 bytes (125 words) - 11:19, 22 November 2018
• M(16,1,1)
  |title = M(16,1,1) - <math>kC_{16}</math> |image = M(2,1,1)quiver.png
  1 KB (172 words) - 15:22, 7 October 2018
• C4:C4
  ...| <math>k(C_4:C_4)</math> || 1 ||10 (8,2) ||1 ||<math>1</math> || || ||1 ||1 ||
  955 bytes (142 words) - 17:05, 28 January 2019
• D16
  ...or defect groups <math>D_8</math> (see [[References|[Er87, Proposition 7.5.1]]]). ...,7,1)]] || <math>k(D_{16})</math> || 1 ||7 ||1 ||<math>1</math> || || || ||1 ||
  2 KB (219 words) - 10:07, 5 October 2018
• M16
  == Blocks with defect group <math>M_{16} \cong \langle x,y|x^8=y^2=1, yx=x^5y \rangle</math> == ...,6,1)]] || <math>kM_{16}</math> || 1 ||10 ||1 ||<math>1</math> || || ||1 ||1 ||
  961 bytes (143 words) - 08:52, 5 October 2018
• C8xC2
  ...</math> ||<math>(C_8 \times C_2):{\rm Aut}(C_8 \times C_2)</math> || ||1 ||1 ||
  976 bytes (150 words) - 11:22, 13 August 2019
• M(8,5,6)
  |title = M(8,5,6) - <math>k((C_2 \times C_2 \times C_2):(C_7:C_3))</math> |image = M(8,5,6)quiver.png
  2 KB (215 words) - 17:23, 21 November 2018
• M(8,5,8)
  |title = M(8,5,8) - <math>B_0(k(\rm Aut (SL_2(8))))</math> |image = M(8,5,8)quiver.png
  4 KB (411 words) - 15:22, 12 April 2019
• M(8,4,1)
  |title = M(8,4,1) - <math>kQ_8</math> |image = M(4,2,1)quiver.png
  1 KB (158 words) - 09:36, 24 May 2022
• M(8,4,2)
  |title = M(8,4,2) - <math>B_0(kSL_2(5))</math> |image = M(4,2,2)quiver.png
  2 KB (265 words) - 09:40, 24 May 2022
• C3xC3
  ...ontain non-principal blocks. Some Picard groups calculated in [[References#M|[Mar]]]. ...||9 ||1 ||<math>1</math> || <math>(C_3 \times C_3):GL_2(3)</math> || ||1 ||1 ||
  6 KB (781 words) - 10:45, 24 May 2022
• D32
  ...or defect groups <math>D_8</math> (see [[References|[Er87, Proposition 7.5.1]]]). ...8,1)]] || <math>k(D_{32})</math> || 1 ||11 ||1 ||<math>1</math> || || || ||1 ||
  2 KB (219 words) - 11:05, 1 November 2018
• M(9,2,1)
  |title = M(9,2,1) - <math>k(C_3 \times C_3)</math> |image = M(4,2,1)quiver.png
  2 KB (185 words) - 18:16, 21 October 2018
• M(9,2,2)
  |title = M(9,2,2) - <math>k(S_3 \times C_3)</math> |image = M(8,3,3)quiver.png
  2 KB (181 words) - 08:45, 23 October 2018
• M(9,2,3)
  |title = M(9,2,3) - <math>k((C_3 \times C_3):C_2)</math> |image = M(9,2,3)quiver.png
  2 KB (230 words) - 08:43, 23 October 2018
• M(9,2,4)
  |title = M(9,2,4) - <math>k(S_3 \times S_3)</math> |image = M(9,2,4)quiver.png
  2 KB (222 words) - 23:26, 2 January 2019
• SD16
  ...ferences|[Er88c], [Er90b]]]). Further work was carried out in [[References#M|[Mac]]], where <math>SD(3 {\cal H})</math> was eliminated, and the block <m ...6,8,1)]] || <math>kSD_{16}</math> || 1 ||7 ||1 ||<math>1</math> || || || ||1 ||
  3 KB (385 words) - 14:34, 4 August 2022
• C(2^m)xC(2^m)
  == Blocks with defect group <math>C_{2^m} \times C_{2^m}</math> for <math>m>1</math> == ...<math>(C_{2^m} \times C_{2^m}):Aut(C_{2^m} \times C_{2^m})</math> || ||1 ||1 ||
  1 KB (181 words) - 08:14, 4 June 2019
• MNA(2,1)
  ...efect group <math>MNA(2,1)=\langle x,y|x^4=y^2=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle</math> == ...rely on the [[Glossary#CFSG|CFSG]]. The automorphism group of <math>MNA(2,1)</math> is a <math>2</math>-group, but by [[References#S|[Sa14,12.7]]] ther
  2 KB (255 words) - 12:47, 9 November 2022
• M(16,3,2)
  |title = M(16,3,2) - <math>B_0(k(A_5:C_4))</math> |defect = [[MNA(2,1)]]
  1 KB (100 words) - 10:51, 15 August 2019
• Q16
  ...6,9,1)]] || <math>kSD_{16}</math> || 1 ||7 ||1 ||<math>1</math> || || || ||1 || ...le cover SmallGroup(240,89)</ref> || ? ||8 ||2 ||<math>1</math> || || || ||1 || <math>Q(2 {\cal A})</math>
  3 KB (368 words) - 12:43, 26 November 2018
• D8xC2
  ...| <math>k(D_8 \times C_2)</math> || ? ||10 ||1 ||<math>1</math> || || || ||1 || ...0(k(PGL_2(5) \times C_2))</math> || ? ||10 ||2 ||<math>1</math> || || || ||1 ||
  1 KB (196 words) - 12:21, 4 January 2019
• Q8xC2
  ...6,9,1)]] || <math>kSD_{16}</math> || 1 ||7 ||1 ||<math>1</math> || || || ||1 || ...le cover SmallGroup(240,89)</ref> || ? ||8 ||2 ||<math>1</math> || || || ||1 || <math>Q(2 {\cal A})</math>
  2 KB (303 words) - 23:31, 15 August 2020
• D8*C4
  ...1)]] || <math>k(Q_8*C_4)</math> || 1 ||10 ||1 ||<math>1</math> || || ||1 ||1 || ...math>B_0(k(SL_2(5)*C_4))</math> || ? ||14 ||3 ||<math>1</math> || || ||1 ||1 ||
  1 KB (192 words) - 12:47, 15 August 2019
• M(16,10,2)
  |title = M(16,10,2) - <math>B_0(k(C_4 \times A_5))</math> |image = M(8,5,2)quiver.png
  2 KB (254 words) - 09:31, 5 December 2018
• M(16,10,3)
  |title = M(16,10,3) - <math>k(C_4 \times A_4)</math> |image = M(8,5,3)quiver.png
  2 KB (220 words) - 23:47, 18 December 2018
• M(9,2,16)
  |title = M(9,2,16) - <math>B_0(kPSL_3(4))</math> |k-morita-frob = 1
  2 KB (197 words) - 18:01, 18 December 2018
• C9xC3
  ...<math>k(C_9 \times C_3)</math> || 1 ||27 ||1 ||<math>1</math> || || ||1 ||1 || ...((C_9 \times C_3):C_2)</math> || ||15 ||2 ||<math>C_2</math> || || ||1 ||1 || Simultaneously inverting elements of <math>C_9</math> and <math>C_3</mat
  1 KB (188 words) - 16:45, 10 January 2019
• 3 +^3
  == Blocks with defect group <math>3_+^{1+2}</math> == ...1)]] || <math>k3_+^{1+2}</math> || 1 ||11 ||1 ||<math>1</math> || || ||1 ||1 ||
  2 KB (182 words) - 21:27, 14 June 2019
• C32
  ...h> ||<math>C_{32}:(C_8 \times C_2)</math> || <math>k^{30}:k^*</math> ||1 ||1 ||
  871 bytes (125 words) - 16:34, 28 January 2019
• MNA(2,2)
  ...efect group <math>MNA(2,2)=\langle x,y|x^4=y^4=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle</math> == ...<math>k(MNA(2,2))</math> || 1 ||20 (16,4) ||1 ||<math>1</math> || || ||1 ||1 ||
  938 bytes (132 words) - 16:46, 28 January 2019
• C8xC4
  ...1 ||<math>1</math> || <math>(C_8 \times C_4):((C_2)^4:D_8)</math> || ||1 ||1 ||
  801 bytes (120 words) - 16:58, 28 January 2019
• C8:C4
  ...<math>k(C_8:C_4)</math> || 1 ||20 (16,4) ||1 ||<math>1</math> || || ||1 ||1 ||
  957 bytes (142 words) - 15:34, 12 April 2019
• MNA(3,1):C2
  ...C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle</math> == ...show that there are no non-trivial saturated fusion systems on <math>MNA(3,1):C_2</math> (see [[References#S|[Sa14]]]). See also [[References#V|[vdW91,
  1 KB (159 words) - 16:02, 12 April 2019
• C16xC2
  ...> ||<math>(C_{16} \times C_2):{\rm Aut}(C_{16} \times C_2)</math> || ||1 ||1 ||
  995 bytes (150 words) - 11:25, 13 August 2019
• (C2)^5
  ...h> || 1 ||32 ||1 ||<math>1</math> || <math>(C_2)^5:GL_5(2)</math> || ||1 ||1 || ...||<math>C_3</math> || <math>((C_2)^3 : GL_3(2)) \times S_3</math> || ||1 ||1 ||
  6 KB (825 words) - 10:18, 17 May 2022
• M(16,3,3)
  |title = M(16,3,3) - <math>k(A_4:C_4)</math><ref><math>A_4:C_4</math> is SmallGroup(48 |defect = [[MNA(2,1)]]
  2 KB (166 words) - 10:56, 15 August 2019
• M(16,14,1)
  |title = M(16,14,1) - <math>k((C_2)^4)</math> |inertialquotients = <math>1</math>
  2 KB (226 words) - 15:42, 28 November 2019
• M(16,14,2)
  |title = M(16,14,2) - <math>k(C_2 \times C_2 \times A_5)</math> |k-morita-frob = 1
  2 KB (301 words) - 14:48, 27 November 2019
• M(16,14,4)
  |title = M(16,14,4) - <math>k((C_2)^4 : C_3)</math> |k-morita-frob = 1
  2 KB (286 words) - 15:07, 27 November 2019
• M(16,14,3)
  |title = M(16,14,3) - <math>k(C_2 \times C_2 \times A_4)</math> |k-morita-frob = 1
  2 KB (277 words) - 15:02, 27 November 2019
• M(16,14,5)
  |title = M(16,14,5) - <math>k((C_2)^4 : C_5)</math> |k-morita-frob = 1
  3 KB (323 words) - 15:21, 27 November 2019
• M(16,14,6)
  |title = M(16,14,6) - <math>k(C_2 \times ((C_2)^3 : C_7))</math> |k-morita-frob = 1
  3 KB (296 words) - 15:53, 27 November 2019
• M(16,14,7)
  |title = M(16,14,7) - <math>B_0(k(C_2 \times SL_2(8)))</math> |k-morita-frob = 1
  4 KB (426 words) - 15:50, 27 November 2019
• M(16,14,8)
  |title = M(16,14,8) - <math>k(A_4 \times A_4)</math> |k-morita-frob = 1
  4 KB (397 words) - 13:56, 28 November 2019
• M(16,14,9)
  |title = M(16,14,9) - <math>B_0(k(A_4 \times A_5))</math> |k-morita-frob = 1
  4 KB (472 words) - 14:13, 28 November 2019
• M(16,14,10)
  |title = M(16,14,10) - <math>B_0(k(A_5 \times A_5))</math> |k-morita-frob = 1
  2 KB (176 words) - 14:19, 28 November 2019
• M(16,14,11)
  |title = M(16,14,11) - <math>k((C_2)^4 : C_{15})</math> |k-morita-frob = 1
  3 KB (194 words) - 18:40, 9 December 2019
• M(16,14,12)
  |title = M(16,14,12) - <math>B_0(k(SL_2(16)))</math> |k-morita-frob = 1
  3 KB (173 words) - 18:40, 9 December 2019
• M(16,14,13)
  |title = M(16,14,13) - <math>k(C_2 \times ((C_2)^3 : (C_7 : C_3)))</math> |k-morita-frob = 1
  3 KB (296 words) - 14:48, 28 November 2019
• M(16,14,14)
  |title = M(16,14,14) - <math>B_0(k(C_2 \times J_1))</math> |k-morita-frob = 1
  3 KB (391 words) - 15:34, 28 November 2019
• M(16,14,15)
  |title = M(16,14,15) - <math>B_0(k(C_2 \times \operatorname{Aut}(SL_2(8))))</math> |k-morita-frob = 1
  3 KB (412 words) - 19:49, 8 December 2019
• M(16,14,16)
  |title = M(16,14,16) - <math>b_2(k((C_2)^4:3^{1+2}_+))</math> |representative = <math>b_2(k((C_2)^4:3^{1+2}_+))</math>
  2 KB (232 words) - 15:40, 28 November 2019
• M(32,51,6)
  |title = M(32,51,6) - <math>k(((C_2)^3 : C_7) \times (C_2)^2)</math> |k-morita-frob = 1
  4 KB (475 words) - 13:05, 6 December 2019
• M(32,51,1)
  |title = M(32,51,1) - <math>k((C_2)^5)</math> |inertialquotients = <math>1</math>
  2 KB (245 words) - 15:17, 5 December 2019
• M(32,51,2)
  |title = M(32,51,2) - <math>k(A_4 \times (C_2)^3)</math> |k-morita-frob = 1
  3 KB (320 words) - 15:26, 5 December 2019
• M(32,51,3)
  |title = M(32,51,3) - <math>B_0(k(A_5 \times (C_2)^3))</math> |k-morita-frob = 1
  3 KB (369 words) - 16:28, 5 December 2019
• M(32,51,4)
  |title = M(32,51,4) - <math>k((C_2)^4 : C_3) \times C_2)</math> |k-morita-frob = 1
  2 KB (319 words) - 16:32, 5 December 2019
• M(32,51,5)
  |title = M(32,51,5) - <math>k((C_2)^4 : C_5) \times C_2)</math> |k-morita-frob = 1
  3 KB (439 words) - 16:54, 9 December 2019
• M(32,51,7)
  |title = M(32,51,7) - <math>B_0(k(SL_2(8) \times (C_2)^2))</math> |k-morita-frob = 1
  5 KB (620 words) - 13:14, 6 December 2019
• M(32,51,8)
  |title = M(32,51,8) - <math>k(A_4 \times A_4 \times C_2)</math> |k-morita-frob = 1
  5 KB (563 words) - 13:25, 6 December 2019
• M(32,51,9)
  |title = M(32,51,9) - <math>B_0(k(A_4 \times A_5 \times C_2))</math> |k-morita-frob = 1
  5 KB (709 words) - 13:27, 6 December 2019
• M(32,51,10)
  |title = M(32,51,10) - <math>B_0(k(A_5 \times A_5 \times C_2))</math> |k-morita-frob = 1
  6 KB (924 words) - 13:37, 6 December 2019
• M(32,51,11)
  |title = M(32,51,11) - <math>k(((C_2)^4 : C_{15}) \times C_2)</math> |k-morita-frob = 1
  8 KB (839 words) - 16:55, 9 December 2019
• M(32,51,12)
  |title = M(32,51,12) - <math>B_0(k(SL_2(16) \times C_2))</math> |k-morita-frob = 1
  5 KB (233 words) - 16:55, 9 December 2019
• M(32,51,13)
  |title = M(32,51,13) - <math>k(((C_2)^3 : C_7) \times A_4)</math> |k-morita-frob = 1
  12 KB (1,029 words) - 16:04, 8 December 2019
• M(32,51,14)
  |title = M(32,51,14) - <math>B_0(k(((C_2)^3 : C_7) \times A_5))</math> |k-morita-frob = 1
  14 KB (1,366 words) - 16:01, 8 December 2019
• M(32,51,15)
  |title = M(32,51,15) - <math>B_0(k(SL_2(8) \times A_4))</math> |k-morita-frob = 1
  15 KB (1,470 words) - 16:13, 8 December 2019
• M(32,51,16)
  |title = M(32,51,16) - <math>B_0(k(SL_2(8) \times A_5))</math> |k-morita-frob = 1
  18 KB (2,005 words) - 17:16, 8 December 2019
• M(32,51,17)
  |title = M(32,51,17) - <math>k(((C_2)^3 : (C_7:C_3) \times (C_2)^2)</math> |k-morita-frob = 1
  3 KB (372 words) - 17:59, 8 December 2019
• M(32,51,18)
  |title = M(32,51,18) - <math>B_0(k(J_1 \times (C_2)^2))</math> |k-morita-frob = 1
  5 KB (568 words) - 19:42, 8 December 2019
• M(32,51,19)
  |title = M(32,51,19) - <math>B_0(k({\rm Aut}(SL_2(8)) \times (C_2)^2))</math> |k-morita-frob = 1
  5 KB (578 words) - 19:49, 8 December 2019
• M(32,51,20)
  |title = M(32,51,20) - <math>k((C_2)^5 : (C_7:C_3))</math> |k-morita-frob = 1
  3 KB (386 words) - 12:42, 9 December 2019
• M(32,51,21)
  |title = M(32,51,21) - <math>B_0(k((SL_2(8) \times (C_2)^2) : C_3))</math> |k-morita-frob = 1
  4 KB (547 words) - 12:42, 9 December 2019
• M(32,51,22)
  |title = M(32,51,22) - <math>k((C_2)^4 : C_{31})</math> |k-morita-frob = 1
  18 KB (1,401 words) - 12:59, 9 December 2019
• M(32,51,23)
  |title = M(32,51,23) - <math>B_0(k(SL_2(32)))</math> |k-morita-frob = 1
  9 KB (172 words) - 13:47, 9 December 2019
• M(32,51,24)
  |title = M(32,51,24) - <math>k(((C_2)^3 : (C_7:C_3)) \times A_4)</math> |k-morita-frob = 1
  8 KB (718 words) - 14:03, 9 December 2019
• M(32,51,25)
  |title = M(32,51,25) - <math>B_0(k(((C_2)^3 : (C_7:C_3)) \times A_5))</math> |k-morita-frob = 1
  9 KB (911 words) - 14:08, 9 December 2019
• M(32,51,26)
  |title = M(32,51,26) - <math>B_0(k(J_1 \times A_4))</math> |k-morita-frob = 1
  4 KB (185 words) - 14:09, 9 December 2019
• M(32,51,27)
  |title = M(32,51,27) - <math>B_0(k(J_1 \times A_5))</math> |k-morita-frob = 1
  4 KB (184 words) - 14:10, 9 December 2019
• M(32,51,28)
  |title = M(32,51,28) - <math>B_0(k({\rm Aut}(SL_2(8)) \times A_4))</math> |k-morita-frob = 1
  4 KB (193 words) - 14:12, 9 December 2019
• M(32,51,29)
  |title = M(32,51,29) - <math>B_0(k({\rm Aut}(SL_2(8)) \times A_5))</math> |k-morita-frob = 1
  4 KB (191 words) - 14:14, 9 December 2019
• M(32,51,30)
  |title = M(32,51,30) - <math>k(((C_2)^5 : (C_{31}:C_5))</math> |k-morita-frob = 1
  5 KB (536 words) - 14:48, 9 December 2019
• M(32,51,31)
  |title = M(32,51,31) - <math>B_0(k({\rm Aut}SL_2(32)))</math> |k-morita-frob = 1
  9 KB (1,187 words) - 17:15, 9 December 2019
• M(32,51,32)
  |title = M(32,51,32) - <math>b_2(k((C_2)^4:3^{1+2}_+) \times C_2)</math> |representative = <math>b_2(k((C_2)^4:3^{1+2}_+) \times C_2)</math>
  2 KB (256 words) - 15:02, 9 December 2019
• M(32,51,33)
  |title = M(32,51,33) - <math>b_2(k((C_2)^5:(C_7:3^{1+2}_+)))</math> |representative = <math>b_2(k((C_2)^5:(C_7:3^{1+2}_+)))</math>
  4 KB (504 words) - 16:08, 9 December 2019
• Fusion-trivial p-groups
  ...>P</math> to be resistant: there exists a central series \[P=P_n \geq P_{n-1} \geq \cdots \geq P_1\] for which each <math>P_i</math> is weakly <math>\ma ...nique subgroup of its isomorphism type. Hence in the sense of [[References#M|[Ma86]]], almost every <math>p</math>-group is fusion trivial. This leaves
  3 KB (455 words) - 16:50, 2 May 2024
• M(32,51,34)
  |title = M(32,51,34) - <math>b_2(k((SL_2(8)\times (C_2)^2):3^{1+2}_+))</math> |representative = <math>b_2(k((SL_2(8)\times (C_2)^2):3^{1+2}_+))</math>
  5 KB (659 words) - 17:08, 9 December 2019
• Guide to contributing: Code
  <div style="font-weight:bold;line-height:1.6;">Magma code</div> G:=SmallGroup(2,1);
  3 KB (489 words) - 20:08, 10 January 2024
• 5 +^3
  == Blocks with defect group <math>5_+^{1+2}</math> == |[[M(125,3,1)]] || <math>k5_+^{1+2}</math> || 1 || 20 || 4 ||1 || <math>1</math> || || ||
  9 KB (993 words) - 10:36, 4 October 2023