Reductions - Revision history

Charles Eaton at 08:34, 3 October 2023

2023-10-03T08:34:17Z

Charles Eaton: Extraspecial

2023-10-03T08:33:20Z

Extraspecial

Charles Eaton at 10:43, 29 June 2020

2020-06-29T10:43:58Z

Charles Eaton: Added Kuslhammer reductions etc.

2020-06-29T10:43:13Z

Added Kuslhammer reductions etc.

Charles Eaton at 22:46, 18 December 2018

2018-12-18T22:46:18Z

Charles Eaton at 17:37, 23 September 2018

2018-09-23T17:37:28Z

Charles Eaton at 17:28, 23 September 2018

2018-09-23T17:28:44Z

Charles Eaton at 13:57, 20 September 2018

2018-09-20T13:57:26Z

Charles Eaton: Created page with "This page will contain descriptions of reduction techniques and results."

2018-08-26T14:18:24Z

Created page with "This page will contain descriptions of reduction techniques and results."

New page

This page will contain descriptions of reduction techniques and results.

@@ Line 22: / Line 22: @@
 '''<math>P</math> abelian:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References#E|[EEL18]]], [[References#F|[FK18]]].
-'''<math>3_+^{1+2}</math>:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for <math>3_+^{1+2}</math>, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with defect groups <math>3_+^{1+2}</math>.
+'''<math>3_+^{1+2}</math>:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for <math>3_+^{1+2}</math>, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with defect groups <math>3_+^{1+2}</math>. See [[References#A|[AE23]]].
 == Weak Donovan conjecture ==
 For arbitrary <math>p</math>-groups, it suffices to check the conjecture for blocks of quasisimple groups with centre of order not divisible by <math>p</math>. See [[References#D|[Du04]]].

@@ Line 22: / Line 22: @@
 '''<math>P</math> abelian:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References#E|[EEL18]]], [[References#F|[FK18]]].
+'''<math>3_+^{1+2}</math>:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for <math>3_+^{1+2}</math>, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with defect groups <math>3_+^{1+2}</math>.
 == Weak Donovan conjecture ==
 For arbitrary <math>p</math>-groups, it suffices to check the conjecture for blocks of quasisimple groups with centre of order not divisible by <math>p</math>. See [[References#D|[Du04]]].

@@ Line 18: / Line 18: @@
 Eisele in [[References#E|[Ei18]]] proved the analogue of [[References#K|[Kü95]]] for the <math>\mathcal{O}</math>-Donovan conjecture, so it suffices to consider blocks of finite groups that are generated by the defect groups.
-By [[References#E|[EL18]]] in order to verify the <math>\mathcal{O}</math>-Donovan conjecture for a <math>p</math>-group <math>P</math> it suffices to check it for blocks of finite groups <math>G</math> with defect group <math>D \cong P</math> and no proper normal subgroup <math>N \triangleleft G</math> such that <math>G=C_D(D \cap N)N</math>.
+By [[References#E|[EL20]]] in order to verify the <math>\mathcal{O}</math>-Donovan conjecture for a <math>p</math>-group <math>P</math> it suffices to check it for blocks of finite groups <math>G</math> with defect group <math>D \cong P</math> and no proper normal subgroup <math>N \triangleleft G</math> such that <math>G=C_D(D \cap N)N</math>.
 '''<math>P</math> abelian:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References#E|[EEL18]]], [[References#F|[FK18]]].

@@ Line 6: / Line 6: @@
 === <math>k</math>-Donovan conjecture ===
 Several reductions were achieved in [[References#D|[Du04]]], but these have been subsumed in later work.
 '''<math>P</math> abelian:''' To show the <math>k</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References#E|[EL18b]]], [[References#F|[FK18]]].
 === <math>\mathcal{O}</math>-Donovan conjecture ===
 '''<math>P</math> abelian:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References#E|[EEL18]]], [[References#F|[FK18]]].
 == Weak Donovan conjecture ==
 For arbitrary <math>p</math>-groups, it suffices to check the conjecture for blocks of quasisimple groups with centre of order not divisible by <math>p</math>. See [[References#D|[Du04]]].

@@ Line 7: / Line 7: @@
 === <math>k</math>-Donovan conjecture ===
-Several reductions were achieved in [[References|[Du04]]], but these have been subsumed in later work.
+Several reductions were achieved in [[References#D|[Du04]]], but these have been subsumed in later work.
-'''<math>P</math> abelian:''' To show the <math>k</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References|[EL18b], [FK18]]].
+'''<math>P</math> abelian:''' To show the <math>k</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References#E|[EL18b]]], [[References#F|[FK18]]].
 === <math>\mathcal{O}</math>-Donovan conjecture ===
-'''<math>P</math> abelian:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References|[EEL18], [FK18]]].
+'''<math>P</math> abelian:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References#E|[EEL18]]], [[References#F|[FK18]]].
 == Weak Donovan conjecture ==
-For arbitrary <math>p</math>-groups, it suffices to check the conjecture for blocks of quasisimple groups with centre of order not divisible by <math>p</math>. See [[References|[Du04]]].
+For arbitrary <math>p</math>-groups, it suffices to check the conjecture for blocks of quasisimple groups with centre of order not divisible by <math>p</math>. See [[References#D|[Du04]]].

← Older revision		Revision as of 17:37, 23 September 2018
Line 7:		Line 7:
	=== <math>k</math>-Donovan conjecture ===		=== <math>k</math>-Donovan conjecture ===

−	'''<math>P</math> abelian:''' To show the <math>k</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture\|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. See [[References\|[EL18b], [FK18]]].	+	Several reductions were achieved in [[References\|[Du04]]], but these have been subsumed in later work.
		+
		+	'''<math>P</math> abelian:''' To show the <math>k</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture\|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References\|[EL18b], [FK18]]].
		+
		+	=== <math>\mathcal{O}</math>-Donovan conjecture ===
		+
		+	'''<math>P</math> abelian:''' To show the <math>\mathcal{O}</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture\|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. We may further assume that the centre of the group is a <math>p'</math>-group. See [[References\|[EEL18], [FK18]]].
		+
		+	== Weak Donovan conjecture ==
		+
		+	For arbitrary <math>p</math>-groups, it suffices to check the conjecture for blocks of quasisimple groups with centre of order not divisible by <math>p</math>. See [[References\|[Du04]]].

← Older revision		Revision as of 17:28, 23 September 2018
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	=== <math>k</math>-Donovan conjecture ===		=== <math>k</math>-Donovan conjecture ===
		+
		+	'''<math>P</math> abelian:''' To show the <math>k</math>-Donovan conjecture for abelian <math>p</math>-groups, it suffices to verify the [[Statements of conjectures#WeakDonovan conjecture\|Weak Donovan conjecture]] for blocks of quasisimple groups with abelian defect groups. See [[References\|[EL18b], [FK18]]].

← Older revision		Revision as of 13:57, 20 September 2018
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	This page will contain descriptions of reduction techniques and results.		This page will contain descriptions of reduction techniques and results.
		+
		+	== Donovan's conjecture ==
		+
		+	[[Statements of conjectures#Donovan's conjecture\|For the statement of the conjecture click here.]]
		+
		+	=== <math>k</math>-Donovan conjecture ===