Status of Donovan's conjecture - Revision history

Charles Eaton: /* Donovan's conjecture by p-group */ Extraspecial and wreathed

2023-10-24T09:06:21Z

‎Donovan's conjecture by p-group: Extraspecial and wreathed

CesareGArdito: /* Donovan's conjecture by p-group */

2022-11-09T18:25:12Z

‎Donovan's conjecture by p-group

Charles Eaton: Added results from [EL20]

2020-06-29T07:59:43Z

Added results from [EL20]

Charles Eaton: /* Weak Donovan conjecture */

2020-02-10T13:42:07Z

‎Weak Donovan conjecture

Charles Eaton: Created weak Donovan section

2019-09-23T15:54:10Z

Created weak Donovan section

Charles Eaton at 22:43, 18 December 2018

2018-12-18T22:43:23Z

Charles Eaton at 14:12, 7 December 2018

2018-12-07T14:12:17Z

Charles Eaton: Added some links

2018-12-07T14:11:25Z

Added some links

Charles Eaton at 07:42, 6 December 2018

2018-12-06T07:42:57Z

Charles Eaton at 08:56, 27 November 2018

2018-11-27T08:56:00Z

@@ Line 36: / Line 36: @@
 |-
 |Metacyclic noncyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References#C|[CG12]]], [[References#S|[Sa12b]]] || All blocks nilpotent
 |}

@@ Line 35: / Line 35: @@
 |Minimal nonabelian <math>2</math>-groups 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]]] ||
 |-
-|Metacyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References#C|[CG12]]], [[References#S|[Sa12b]]] || All blocks nilpotent
+|Metacyclic noncyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References#C|[CG12]]], [[References#S|[Sa12b]]] || All blocks nilpotent
 |}

@@ Line 26: / Line 26: @@
 |-
 |<math>Q_8</math> || <math>\mathcal{O}</math> || No || [[References#E|[Er88a]]], [[References#E|[Er88b]]], [[References#K|[HKL07]]], [[References#E|[Ei16]]] ||
 |-
 |Generalised quaternion <math>2</math>-groups || No || No || [[References#E|[Er88a], [Er88b]]] || Donovan's conjecture over <math>\mathcal{O}</math> known if <math>l(B) \neq 2</math><ref>When <math>l(B) \neq 2</math>, each <math>k</math>-Morita equivalence class lifts uniquely to <math>\mathcal{O}</math> by [[References|[Ei16]]].</ref>

@@ Line 68: / Line 68: @@
 == Weak Donovan conjecture ==
-As described in [[References #D|[Dü04]]] the [[Statements of conjectures #Weak Donovans conjecture|Weak Donovan conjecture]] is equivalent to [[Statements of conjectures #Weak Donovans conjecture|bounding the dimensions of the Ext spaces between simple modules]] and [[Statements of conjectures #Weak Donovans conjecture|bounding the Loewy length]]. See [[References #G|[GT19]]] for progress on the former problem.
+As described in [[References #D|[Dü04]]] the [[Statements of conjectures #Weak Donovans conjecture|Weak Donovan conjecture]] is equivalent to [[Statements of conjectures #Weak Donovans conjecture|bounding the dimensions of the Ext spaces between simple modules]] and [[Statements of conjectures #Weak Donovans conjecture|bounding the Loewy length]]. See [[References #G|[GT19]]] and [[References #S|[Sh20]]] for progress on the former problem.
 == Notes ==
 <references />

@@ Line 65: / Line 65: @@
 |Arbitrary groups || Blocks with [[Glossary#Trivial intersection subgroup|trivial intersection]] defect groups || <math>\mathcal{O}</math> || No || [[References#A|[AE04]]] ||
 |}
 == Notes ==
 <references />

@@ Line 13: / Line 13: @@
 ! scope="col"| Notes
 |-
-|Cyclic <math>p</math>-groups || <math>\mathcal{O}</math> || Yes || [[References|[Li96]]] ||
+|Cyclic <math>p</math>-groups || <math>\mathcal{O}</math> || Yes || [[References#L|[Li96]]] ||
 |-
-|<math>C_2 \times C_2</math> || <math>\mathcal{O}</math> || Yes || [[References|[CEKL11]]] || Donovan's conjecture without CFSG, Puig using CFSG
+|<math>C_2 \times C_2</math> || <math>\mathcal{O}</math> || Yes || [[References#C|[CEKL11]]] || Donovan's conjecture without CFSG, Puig using CFSG
 |-
-|Abelian <math>2</math>-groups || <math>\mathcal{O}</math> || No || [[References|[EEL18]]] ||
+|Abelian <math>2</math>-groups || <math>\mathcal{O}</math> || No || [[References#E|[EEL18]]] ||
 |-
-|Abelian <math>3</math>-groups || No || No || [[References|[Ko03]]] || Puig's conjecture known for principal blocks
+|Abelian <math>3</math>-groups || No || No || [[References#K|[Ko03]]] || Puig's conjecture known for principal blocks
 |-
-|Dihedral <math>2</math>-groups || <math>k</math> || No || [[References|[Er87]]] ||
+|Dihedral <math>2</math>-groups || <math>k</math> || No || [[References#E|[Er87]]] ||
 |-
-|Semidihedral <math>2</math>-groups || <math>k</math> || No || [[References|[Er88c], [Er90b]]] ||
+|Semidihedral <math>2</math>-groups || <math>k</math> || No || [[References#E|[Er88c], [Er90b]]] ||
 |-
-|<math>Q_8</math> || <math>\mathcal{O}</math> || No || [[References|[Er88a], [Er88b], [HKL07], [Ei16]]] ||
+|<math>Q_8</math> || <math>\mathcal{O}</math> || No || [[References#E|[Er88a]]], [[References#E|[Er88b]]], [[References#K|[HKL07]]], [[References#E|[Ei16]]] ||
 |-
-|Generalised quaternion <math>2</math>-groups || No || No || [[References|[Er88a], [Er88b]]] || Donovan's conjecture over <math>\mathcal{O}</math> known if <math>l(B) \neq 2</math><ref>When <math>l(B) \neq 2</math>, each <math>k</math>-Morita equivalence class lifts uniquely to <math>\mathcal{O}</math> by [[References|[Ei16]]].</ref>
+|Generalised quaternion <math>2</math>-groups || No || No || [[References#E|[Er88a], [Er88b]]] || Donovan's conjecture over <math>\mathcal{O}</math> known if <math>l(B) \neq 2</math><ref>When <math>l(B) \neq 2</math>, each <math>k</math>-Morita equivalence class lifts uniquely to <math>\mathcal{O}</math> by [[References|[Ei16]]].</ref>
 |-
-|Minimal nonabelian <math>2</math>-groups 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|[EKS12]]] ||
+|Minimal nonabelian <math>2</math>-groups 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]]] ||
 |-
-|Metacyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References|[CG12], [Sa12b]]] || All blocks nilpotent
+|Metacyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References#C|[CG12]]], [[References#S|[Sa12b]]] || All blocks nilpotent
 |}
@@ Line 49: / Line 49: @@
 ! scope="col"| Notes
 |-
-|<math>p</math>-solvable groups || All || <math>\mathcal{O}</math> || Yes || Over <math>k</math> by [[References|[Ku81]]], Puig's conjecture by [[References|[Pu09]]] || See [[References|[Li18d,10.6.2]]]
+|<math>p</math>-solvable groups || All || <math>\mathcal{O}</math> || Yes || Over <math>k</math> by [[References|[Ku81]]], Puig's conjecture by [[References|[Pu09]]] || See [[References#L|[Li18d,10.6.2]]]
 |-
-|Symmetric groups || All || <math>\mathcal{O}</math> || Yes || Over <math>k</math> by [[References|[Sc91]]], Puig's conjecture by [[References|[Pu94]]] ||
+|Symmetric groups || All || <math>\mathcal{O}</math> || Yes || Over <math>k</math> by [[References#S|[Sc91]]], Puig's conjecture by [[References#P|[Pu94]]] ||
 |-
-|Double covers of symmetric groups || All || <math>\mathcal{O}</math> || Yes || [[References|[Ke96]]] ||
+|Double covers of symmetric groups || All || <math>\mathcal{O}</math> || Yes || [[References#K|[Ke96]]] ||
 |-
-|Alternating groups and their double covers || All || <math>\mathcal{O}</math> || Yes || [[References|[Ke02], [Ke96]]] ||
+|Alternating groups and their double covers || All || <math>\mathcal{O}</math> || Yes || [[References#K|[Ke02], [Ke96]]] ||
 |-
-|<math>GL_n(q)</math> for fixed <math>q</math> || Unipotent blocks || <math>\mathcal{O}</math> || Yes || Over <math>k</math> by [[References|[Jo96]]], Puig's conjecture by [[References|[Ke01]]] ||
+|<math>GL_n(q)</math> for fixed <math>q</math> || Unipotent blocks || <math>\mathcal{O}</math> || Yes || Over <math>k</math> by [[References#J|[Jo96]]], Puig's conjecture by [[References#K|[Ke01]]] ||
 |-
-|Classical groups || Unipotent blocks for linear primes || <math>\mathcal{O}</math> || Yes || [[References|[HK00], [HK05]]] || Detailed results beyond those stated here
+|Classical groups || Unipotent blocks for linear primes || <math>\mathcal{O}</math> || Yes || [[References#H|[HK00], [HK05]]] || Detailed results beyond those stated here
 |-
-|Weyl groups of type <math>B, D</math> || All || <math>\mathcal{O}</math> || Yes || [[References|[Ke00]]] ||
+|Weyl groups of type <math>B, D</math> || All || <math>\mathcal{O}</math> || Yes || [[References#K|[Ke00]]] ||
 |-
-|Arbitrary groups || Blocks with [[Glossary#Trivial intersection subgroup|trivial intersection]] defect groups || <math>\mathcal{O}</math> || No || [[References|[AE04]]] ||
+|Arbitrary groups || Blocks with [[Glossary#Trivial intersection subgroup|trivial intersection]] defect groups || <math>\mathcal{O}</math> || No || [[References#A|[AE04]]] ||
 |}

@@ Line 38: / Line 38: @@
 In the table, the column headed Donovan's conjecture indicates whether the conjecture is known over <math>k</math> or <math>\mathcal{O}</math>.
-Note that knowing the <math>\mathcal{O}</math>-Donovan conjecture or [[Statements of conjectures #Donovan's conjecture|Puig's conjecture]] for blocks for a class of groups does not necessarily mean that the <math>\mathcal{O}</math>-lifts or source algebras of the <math>k</math>-Morita equivalence classes involved are known. This is only known for elements of the Morita equivalence class which occur as blocks of groups in that class.
+Note that knowing the <math>\mathcal{O}</math>-Donovan conjecture or [[Statements of conjectures #Puig's conjecture|Puig's conjecture]] for blocks for a class of groups does not necessarily mean that the <math>\mathcal{O}</math>-lifts or source algebras of the <math>k</math>-Morita equivalence classes involved are known. This is only known for elements of the Morita equivalence class which occur as blocks of groups in that class.
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