Results on classes of groups - Revision history

Charles Eaton at 15:35, 5 September 2018

2018-09-05T15:35:49Z

Charles Eaton: Mcbssce moved page Generic classifications by p-group class to Results on classes of groups over redirect: revert

2018-09-05T15:25:59Z

Mcbssce moved page Generic classifications by p-group class to Results on classes of groups over redirect: revert

Charles Eaton at 15:23, 5 September 2018

2018-09-05T15:23:58Z

Charles Eaton at 13:52, 31 August 2018

2018-08-31T13:52:10Z

Charles Eaton: Mcbssce moved page Results on classes of groups to Generic classifications by p-group class

2018-08-31T09:54:07Z

Mcbssce moved page Results on classes of groups to Generic classifications by p-group class

Charles Eaton: Created page with "One approach to Donovan's conjecture is to restrict attention to blocks lying in a given class of finite groups, e.g., $p$ -solvable groups or a family of finite gro..."

2018-08-26T14:23:00Z

Created page with "One approach to Donovan's conjecture is to restrict attention to blocks lying in a given class of finite groups, e.g., <math>p</math>-solvable groups or a family of finite gro..."

New page

One approach to Donovan's conjecture is to restrict attention to blocks lying in a given class of finite groups, e.g., <math>p</math>-solvable groups or a family of finite groups of Lie type. This page will contain information on such results.

← Older revision		Revision as of 15:35, 5 September 2018
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−	This page will contain results ~~for generic classes of ''p''-groups. It is very much under construction so the list below is not complete.~~	+	This page will contain results about Morita equivalence classes amongst blocks of groups belonging to certain classes or families, for example groups of Lie type or <math>p</math>-solvable groups.
−
−	~~== Cyclic ''p''-groups ==~~
−
−	Morita equivalence classes ~~are labelled by [[Brauer trees]], but it is at present an open problem as to which Brauer trees are realised by~~ blocks of ~~finite~~ groups~~. Each ''k''-Morita equivalence class corresponds~~ to ~~an unique <math>\mathcal{O}</math>-Morita equivalence class.~~
−
−	~~== Tame blocks ==~~
−
−	~~Erdmann classified algebras which are candidates~~ for ~~[[Basic algebras\|basic algebras]]~~ of ~~tame blocks, i.e., those with dihedral, semidihedral~~ or generalised quaternion defect groups (see [[References\|[Er90] ]]) and in the cases of dihedral and semihedral defect groups determined which are realised by blocks of finite groups. In the case of generalised quaternion groups, the case of blocks with two simple modules is still open. These classifications only hold with respect to the field ''k'' at present.
−
−	~~== Abelian ''2''-groups with ''2''-rank at most three ==~~
−
−	~~These have been classified in [[References\|[WZZ18] ]] and [[References\|[EL18a] ]] with respect to~~ <math>~~\mathcal{O}~~</math>.
−
−	~~== Abelian ''2''~~-groups ==
−
−	~~Donovan's conjecture holds for ''2''-blocks with abelian defect groups. Some generic classification results are known for certain inertial quotients. These will be detailed here~~.

← Older revision		Revision as of 15:23, 5 September 2018
Line 1:		Line 1:
−	This page will contain generic classifications.	+	This page will contain results for generic classes of ''p''-groups. It is very much under construction so the list below is not complete.
		+
		+	== Cyclic ''p''-groups ==
		+
		+	Morita equivalence classes are labelled by [[Brauer trees]], but it is at present an open problem as to which Brauer trees are realised by blocks of finite groups. Each ''k''-Morita equivalence class corresponds to an unique <math>\mathcal{O}</math>-Morita equivalence class.
		+
		+	== Tame blocks ==
		+
		+	Erdmann classified algebras which are candidates for [[Basic algebras\|basic algebras]] of tame blocks, i.e., those with dihedral, semidihedral or generalised quaternion defect groups (see [[References\|[Er90] ]]) and in the cases of dihedral and semihedral defect groups determined which are realised by blocks of finite groups. In the case of generalised quaternion groups, the case of blocks with two simple modules is still open. These classifications only hold with respect to the field ''k'' at present.
		+
		+	== Abelian ''2''-groups with ''2''-rank at most three ==
		+
		+	These have been classified in [[References\|[WZZ18] ]] and [[References\|[EL18a] ]] with respect to <math>\mathcal{O}</math>.
		+
		+	== Abelian ''2''-groups ==
		+
		+	Donovan's conjecture holds for ''2''-blocks with abelian defect groups. Some generic classification results are known for certain inertial quotients. These will be detailed here.

← Older revision		Revision as of 13:52, 31 August 2018
Line 1:		Line 1:
−	~~One approach to Donovan's conjecture is to restrict attention to blocks lying in a given class of finite groups, e.g., <math>p</math>-solvable groups or a family of finite groups of Lie type.~~ This page will contain ~~information on such results~~.	+	This page will contain generic classifications.

← Older revision	Revision as of 15:25, 5 September 2018
(No difference)

← Older revision	Revision as of 09:54, 31 August 2018
(No difference)