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Create the page "Blocks with cyclic defect group" on this wiki! See also the search results found.

• C2
  == Blocks with defect group <math>C_2</math> == These are blocks with [[Blocks with cyclic defect groups|cyclic defect groups]] and so they are described by [[Brauer trees]].
  868 bytes (126 words) - 22:59, 21 November 2018
• C3
  == Blocks with defect group <math>C_3</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  1 KB (154 words) - 11:20, 22 November 2018
• C4
  == Blocks with defect group <math>C_4</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  880 bytes (129 words) - 11:18, 22 November 2018
• C9
  == Blocks with defect group <math>C_9</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  1 KB (168 words) - 11:27, 22 November 2018
• References
  ...4] || '''Jianbei An and C. W. Eaton''', ''Blocks with trivial intersection defect groups'', Math. Z. '''247''' (2004), 461-486. ...rg/abs/2310.02150 ''Morita equivalence classes of blocks with extraspecial defect groups <math>p_+^{1+2}</math>''], [https://arxiv.org/abs/2310.02150 arxiv:2
  21 KB (2,957 words) - 12:29, 2 May 2024
• Status of Donovan's conjecture
  == Donovan's conjecture by <math>p</math>-group == |Cyclic <math>p</math>-groups || <math>\mathcal{O}</math> || Yes || [[References#L|
  5 KB (727 words) - 10:06, 24 October 2023
• C5
  == Blocks with defect group <math>C_5</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  1 KB (205 words) - 11:28, 22 November 2018
• Open problems
  ...e is for open problems, large and small, relating to module categories for blocks. Missing data is also flagged within tables elsewhere on this site. ...e isomorphism type of a defect group|Is the isomorphism type of the defect group a Morita invariant?]] - no (see [[References#G|[GMdelR21]]])
  1 KB (178 words) - 12:30, 21 June 2021
• C8
  == Blocks with defect group <math>C_8</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  857 bytes (125 words) - 11:19, 22 November 2018
• C25
  == Blocks with defect group <math>C_{25}</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  2 KB (229 words) - 11:31, 22 November 2018
• M(3,1,1)
  |defect = [[C3|<math>C_3</math>]] |defect-morita-inv? = Yes
  2 KB (225 words) - 15:59, 7 October 2018
• M(2,1,1)
  |defect = [[C2|<math>C_2</math>]] |defect-morita-inv? = Yes
  2 KB (230 words) - 13:18, 9 September 2018
• Generic classifications by p-group class
  ...ollowing [[References#V|[vdW91]]] (where ''p''-groups for which any finite group <math>G</math> containing <math>P</math> as a Sylow ''p''-subgroup must be ...ust be nilpotent and so Morita equivalent to the group algebra of a defect group by [[References#P|[Pu88]]].
  11 KB (1,772 words) - 12:15, 9 January 2024
• C27
  == Blocks with defect group <math>C_{27}</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  1 KB (148 words) - 11:26, 22 November 2018
• Glossary
  Morita/stable equivalence of blocks induced by a bimodule which has endopermutation source. ...or a block <math>B</math> (sometimes calle the Brauer category) is defined with respect to a maximal subpair <math>(D,b_D)</math>, and is written <math>\ma
  5 KB (841 words) - 23:02, 18 November 2020
• C(3^n)
  == Blocks with defect group <math>C_{3^n}</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  2 KB (257 words) - 23:34, 2 January 2019
• Labelling for Morita equivalence classes
  ...ystems for labelling Morita equivalence classes of blocks of finite groups with respect to an algebraically closed field <math>k</math>. === When the defect group is listed in the GAP SmallGroup library ===
  3 KB (477 words) - 11:08, 3 October 2023
• C7
  == Blocks with defect group <math>C_7</math> == ...o they are described by [[Brauer trees]]. There are candidate Brauer trees with no known block realising them.
  4 KB (465 words) - 12:58, 22 November 2018
• Other resources
  ...archive] of blocks of simple groups, kept at RWTH Aachen by Thomas Breuer, with information extracted from the GAP library. ...ing, symmetric and sporadic groups, as well as lists of blocks with cyclic defect groups.
  1 KB (190 words) - 15:36, 16 January 2019
• C16
  == Blocks with defect group <math>C_{16}</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  871 bytes (125 words) - 11:19, 22 November 2018
• Known Picard groups
  ...G</math> for a finite group <math>G</math>. Let <math>D</math> be a defect group and let <math>E</math> be the inertial quotient. == Blocks with cyclic groups ==
  3 KB (577 words) - 12:04, 25 May 2021
• Tame blocks
  ...e a block of <math>kG</math> for a finite group <math>G</math> with defect group <math>D</math>. Then ...h>B</math> has finite representation type if and only if <math>D</math> is cyclic.
  3 KB (427 words) - 19:28, 9 November 2022
• To do list
  *[[Blocks with cyclic defect groups]]. This background section has only just been started. Also [[Brauer *[[Tame blocks]]. This background section contains only basic information, and is not refe
  1,009 bytes (152 words) - 18:46, 9 December 2019
• C32
  == Blocks with defect group <math>C_{32}</math> == These are [[blocks with cyclic defect groups]] and so they are described by [[Brauer trees]].
  871 bytes (125 words) - 16:34, 28 January 2019
• About the site
  ...finite simple groups to Donovan's conjecture and to the classification of blocks of finite groups up to Morita equivalence. ...is not fully understood. Some wild cases are understood because the defect group forces the block to be nilpotent, using fusion arguments. In the remaining
  1 KB (207 words) - 13:19, 24 September 2019
• A few thoughts on the Donovan conjecture
  ...position numbers that could occur, again with prescribed isotype of defect group. This latter was in fact incorrect. ...bras with at most three isotypes of irreducibles. This led to my Dihedral Defect Groups paper, which (sort of) showed that the bounding of the Cartan matrix
  4 KB (596 words) - 16:21, 21 August 2020
• (Non-)Morita invariance of the isomorphism type of a defect group
  ...nce the group algebras of p-groups are basic, it follows directly that the group algebras a Morita equivalent. ...examples is SmallGroup(512,453) and SmallGroup(512,456). These groups have cyclic derived subgroup of order four and nilpotency class three. They have presen
  1 KB (204 words) - 12:30, 21 June 2021