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• Main Page
  <!-- BANNER ACROSS TOP OF PAGE --> <div style="font-size:170%; font-weight:bold; padding:.1em;">Blocks of finite groups</div>
  4 KB (500 words) - 22:10, 18 November 2020
• Statements of conjectures
  ...ed, and it is no loss to assume it is the algebraic closure <math>k</math> of the field with <math>p</math> elements, as in [[Notation|the notation secti ...ssible Morita equivalence classes for blocks of <math>kG</math> for finite groups G with defect group isomorphic to <math>P</math>.
  6 KB (970 words) - 16:15, 21 August 2020
• References
  ...n''', ''Local representation theory'', The Santa Cruz Conference on Finite Groups., Proc. Sympos. Pure Math. '''37''' (1980), 369-375. ...''Jianbei An and C. W. Eaton''', ''Blocks with trivial intersection defect groups'', Math. Z. '''247''' (2004), 461-486.
  21 KB (2,953 words) - 12:20, 9 January 2024
• Notation
  ..., but this condition can usually be avoided. In general however the choice of <math>\mathcal{O}</math> is not consistent across the literature and some c ...s not otherwise clear from context <math>kB</math> will refer to the block of <math>kG</math>.
  3 KB (444 words) - 18:45, 9 December 2019
• Reductions
  This page will contain descriptions of reduction techniques and results. [[Statements of conjectures#Donovan's conjecture|For the statement of the conjecture click here.]]
  2 KB (394 words) - 09:34, 3 October 2023
• Blocks
  == Blocks == ...of <math>kG</math>. In some situations it will be the corresponding block of <math>\mathcal{O}G</math>.
  503 bytes (83 words) - 09:28, 21 September 2018
• Generic classifications by p-group class
  This page contains results for classes of ''p''-groups for which we either have classifications or have general results concerning == Fusion trivial ''p''-groups ==
  11 KB (1,772 words) - 12:15, 9 January 2024
• Glossary
  Morita/stable equivalence of blocks induced by a bimodule which has endopermutation source. The classification of finite simple groups.
  5 KB (841 words) - 23:02, 18 November 2020
• Labelling for Morita equivalence classes
  ...tible systems for labelling Morita equivalence classes of blocks of finite groups with respect to an algebraically closed field <math>k</math>. M(x,y,z) is a class consisting of blocks with defect groups of order x, with a representative having defect group SmallGroup(x,y) in GAP/M
  3 KB (477 words) - 11:08, 3 October 2023
• Miscallaneous results
  == Blocks with basic algebras of low dimension == ...h basic algebras of low dimension|Main article: Blocks with basic algebras of low dimension]]
  2 KB (289 words) - 14:51, 4 August 2022
• Blocks with basic algebras of low dimension
  == Blocks with basic algebras of dimension at most 16 == ...e a classification for dimensions 15 and 16, except for one unsettled case of a block with defect group <math>C_{13}</math> in dimension 15.
  4 KB (528 words) - 14:33, 13 December 2023
• Known Picard groups
  Let <math>B</math> be a block of <math>\mathcal{O}G</math> for a finite group <math>G</math>. Let <math>D</math> be a defect group and let <math>E< == Blocks with cyclic groups ==
  3 KB (577 words) - 12:04, 25 May 2021
• Tame blocks
  ...math>. The properties of having finite or infinite representation type and of being tame or wild are all Morita invariants. Let <math>B</math> be a block of <math>kG</math> for a finite group <math>G</math> with defect group <math>D</math>. Then
  3 KB (427 words) - 19:28, 9 November 2022
• Morita invariants
  == Invariants preserved under Morita equivalence of blocks of f.d. <math>k</math>-algebras == * Number of isomorphism classes of simple modules
  2 KB (241 words) - 11:48, 4 January 2019
• (C2)^5
  == Blocks with defect group <math>(C_2)^5</math> == ...8c]]] or using the main theorem of [[References#L|[Liv19]]]. TO DO: PICARD GROUPS COMPUTED AND FILLED IN WHERE METHOD KNOWN
  6 KB (825 words) - 10:18, 17 May 2022
• About the site
  ...oups to Donovan's conjecture and to the classification of blocks of finite groups up to Morita equivalence. ...sion arguments. In the remaining cases the classification of finite simple groups is required.
  1 KB (207 words) - 13:19, 24 September 2019
• A few thoughts on the Donovan conjecture
  ...the decomposition numbers that could occur, again with prescribed isotype of defect group. This latter was in fact incorrect. ...my Dihedral Defect Groups paper, which (sort of) showed that the bounding of the Cartan matrix (and so the decomposition matrix) was possible in this ca
  4 KB (596 words) - 16:21, 21 August 2020