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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
  • 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
  • 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
  • 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>
    6 KB (970 words) - 16:15, 21 August 2020
  • Classification by p-group
    | <strong><math>1 \leq |D| \leq 8</math> &nbsp;</strong> | 1 || 1 || <math>1</math> || 1(1) || <math>\mathcal{O}</math> || <math>\mathcal{O}</math> || ||
    33 KB (3,797 words) - 19:59, 10 January 2024
  • 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
    ...and Quillen's dimension theorem'', J. Pure Appl. Algebra '''22''' (1981), 1-9. ...a equivalence classes of blocks with extraspecial defect groups <math>p_+^{1+2}</math>''], [https://arxiv.org/abs/2310.02150 arxiv:2310.02150]
    21 KB (2,957 words) - 12:29, 2 May 2024
  • Status of Donovan's conjecture
    ...of the form <math>\langle x,y:x^{2^r}=y^{2^r}=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle</math> || <math>\mathcal{O}</math> || No || [[References#E|[EKS12]] |<math>p_+^{1+2}</math> for <math>p \geq 5</math> || <math>\mathcal{O}</math> || No || [[
    5 KB (727 words) - 10:06, 24 October 2023
  • 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
  • Reductions
    ...onjecture]] for blocks of quasisimple groups with defect groups <math>3_+^{1+2}</math>. See [[References#A|[AE23]]].
    2 KB (394 words) - 09:34, 3 October 2023
  • 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)
    |k-morita-frob = 1 2 & 2 & 1 \\
    2 KB (309 words) - 15:47, 4 January 2019
  • M(4,2,3)
    |k-morita-frob = 1 2 & 1 & 1 \\
    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
    |[[C(2^n)|<math>C_{2^n}</math>]] || 1 || 1 || Yes || [[References#L|[Li96]]] || [[Blocks with cyclic defect groups]] |[[C(2^m)xC(2^n)|<math>C_{2^m} \times C_{2^n}</math>]] || 1 || 1 || Yes || [[References#P|[Pu88]]] || [[Nilpotent blocks]]
    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>. ...groups such that every proper subgroup is abelian. For <math>r \geq s \geq 1</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)
    |k-morita-frob = 1 1 & 0 & 0 \\
    3 KB (344 words) - 22:07, 5 December 2018
  • Labelling for Morita equivalence classes
    ...on M(<math>|P|</math>,1,z) since cyclic <math>p</math>-groups are labelled 1 in the SmallGroup library.
    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)
    |k-morita-frob = 1 1 & 0 & 0 \\
    2 KB (290 words) - 15:51, 3 June 2021
  • M(8,5,2)
    |k-morita-frob = 1 1 & 0 & 0 \\
    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)
    |k-morita-frob = 1 2 & 1 & 1 & 1 & 1 & 1 & 1 \\
    4 KB (595 words) - 10:09, 5 June 2019
  • M(8,5,5)
    |k-morita-frob = 1 4 & 4 & 2 & 2 & 0 & 2 & 1 \\
    3 KB (387 words) - 17:22, 21 November 2018
  • M(8,3,4)
    |inertialquotients = <math>1</math> |k-morita-frob = 1
    2 KB (218 words) - 17:51, 4 October 2018
  • M(8,3,2)
    |image = M(5,1,3)quiver.png |inertialquotients = <math>1</math>
    2 KB (187 words) - 15:09, 4 October 2018
  • M(8,3,3)
    |inertialquotients = <math>1</math> |k-morita-frob = 1
    2 KB (205 words) - 23:53, 18 December 2018
  • M(8,5,7)
    |k-morita-frob = 1 4 & 4 & 3 & 3 & 1 \\
    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)
    |k-morita-frob = 1 1 & 0 & 0 \\
    2 KB (237 words) - 10:57, 28 July 2019
  • M(8,3,6)
    |inertialquotients = <math>1</math> |k-morita-frob = 1
    2 KB (232 words) - 21:48, 4 October 2018
  • M(8,3,5)
    |inertialquotients = <math>1</math> |k-morita-frob = 1
    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)
    |k-morita-frob = 1 2 & 0 & 0 & 1 & 1 \\
    2 KB (215 words) - 17:23, 21 November 2018
  • M(8,5,8)
    |k-morita-frob = 1 1 & 0 & 0 & 0 & 0 \\
    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)
    |k-morita-frob = 1 0 & 1 & 0 \\
    2 KB (265 words) - 09:40, 24 May 2022
  • C3xC3
    ...o03]]] using the [[Glossary#CFSG|CFSG]]. This accounts for classes [[M(9,2,1)]] to [[M(9,2,22)]]. Note that it does not follow from the results in [[Ref ...||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)
    |k-morita-frob = 1 1 & 0 \\
    2 KB (181 words) - 08:45, 23 October 2018
  • M(9,2,3)
    |k-morita-frob = 1 1 & 0 \\
    2 KB (230 words) - 08:43, 23 October 2018
  • M(9,2,4)
    |k-morita-frob = 1 4 & 2 & 1 & 2 \\
    2 KB (222 words) - 23:26, 2 January 2019
  • SD16
    ...6,8,1)]] || <math>kSD_{16}</math> || 1 ||7 ||1 ||<math>1</math> || || || ||1 || ...]] || <math>B_5(kPSU_3(5))</math> || ? ||8 ||2 ||<math>1</math> || || || ||1 || <math>SD(2 {\cal A})_1</math>
    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
  • Known Picard groups
    If <math>E=1</math>, then <math>B</math> is nilpotent and so <math>{\rm Pic}(B)\cong D:{ ...morphic to a subgroup of <math>E</math> and [[References#B|[BKL18, Theorem 1.4]]] gives a generator of this subgroup, it still needs to be computed on a
    3 KB (577 words) - 12:04, 25 May 2021
  • 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)
    |defect = [[MNA(2,1)]] |inertialquotients = <math>1</math>
    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)
    |k-morita-frob = 1 0 & 1 & 0 \\
    2 KB (254 words) - 09:31, 5 December 2018
  • M(16,10,3)
    |k-morita-frob = 1 1 & 0 & 0 \\
    2 KB (220 words) - 23:47, 18 December 2018
  • Groups of perfect self-isometries
    ...}^+(B)</math> defined in [[References|[Ru11]]]). If <math>{\rm Piccent}(B)=1</math>, then <math>{\rm Pic}(B)</math> embeds into <math>{\rm PI}_+(B)</mat
    905 bytes (153 words) - 10:40, 6 December 2018
  • M(9,2,16)
    |k-morita-frob = 1 2 & 1 & 1 & 1 & 2 \\
    2 KB (197 words) - 18:01, 18 December 2018
  • Nilpotent blocks
    ...n. Then <math>B</math> is nilpotent if and only if <math>N_G(D,b_D)/C_G(D)=1</math>. ...ces#P|[Pu88]]].</ref> Consequently, a nilpotent block satisfies <math>l(B)=1</math> and its decomposition and Cartan matrices are determined.
    2 KB (457 words) - 10:41, 19 December 2018

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