Status of Donovan's conjecture - Revision history

Charles Eaton at 10:30, 8 October 2026

2026-10-08T10:30:50Z

Charles Eaton: OpenAI claim

2026-10-08T10:18:04Z

OpenAI claim

Charles Eaton: Applications of [EEKLS26], Suzuki 2-groups

2026-08-13T15:14:01Z

Applications of [EEKLS26], Suzuki 2-groups

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

@@ Line 3: / Line 3: @@
 == Donovan's conjecture by <math>p</math>-group ==
-In October 2026 OpenAI released a claimed proof of Donovan's conjecture, with different manuscripts for <math>k</math> and <math>\mathcal{O}</math>, using the classification of finite simple groups. As of 8/10/2026 we are still attempting to check/understand the proof, and this is likely to take some time (especially since we are simultaneously interested in the claimed proof of Alperin's weight conjecture!). Below is an account of progress made before or independently of  the OpenAI proof.
+In October 2026 OpenAI released a claimed proof of Donovan's conjecture, with different manuscripts for <math>k</math> ([[References#O|[OpenAI26a]]]) and <math>\mathcal{O}</math> ([[References#O|[OpenAI26b]]]), using the classification of finite simple groups. As of 8/10/2026 we are still attempting to check/understand the proof, and this is likely to take some time (especially since we are simultaneously interested in the claimed proof of Alperin's weight conjecture!). Puig's conjecture is open, and the OpenAI manuscripts make no claims on this. Below is an account of progress made before or independently of  the OpenAI proof.
 In the following, the column headed [[Statements of conjectures #Donovan's conjecture|Donovan's conjecture]] indicates whether the conjecture is known over <math>k</math> or <math>\mathcal{O}</math>.

← Older revision		Revision as of 10:18, 8 October 2026
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	== Donovan's conjecture by <math>p</math>-group ==		== Donovan's conjecture by <math>p</math>-group ==
		+
		+	In October 2026 OpenAI released a claimed proof of Donovan's conjecture, with different manuscripts for <math>k</math> and <math>\mathcal{O}</math>, using the classification of finite simple groups. As of 8/10/2026 we are still attempting to check/understand the proof, and this is likely to take some time (especially since we are simultaneously interested in the claimed proof of Alperin's weight conjecture!). Below is an account of progress made before or independently of the OpenAI proof.

	In the following, the column headed [[Statements of conjectures #Donovan's conjecture\|Donovan's conjecture]] indicates whether the conjecture is known over <math>k</math> or <math>\mathcal{O}</math>.		In the following, the column headed [[Statements of conjectures #Donovan's conjecture\|Donovan's conjecture]] indicates whether the conjecture is known over <math>k</math> or <math>\mathcal{O}</math>.

@@ Line 21: / Line 21: @@
 |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#E|[Er87]]] ||
+|Dihedral <math>2</math>-groups || <math>\mathcal{O}</math> || No || [[References#E|[Er87]]], [[References#E|[EEKLS26]] || Full result over <math>\mathcal{O}</math> not formally stated in literature but see discussion in [[References#E|[EEKLS26]]]
 |-
 |Semidihedral <math>2</math>-groups || <math>k</math> || No || [[References#E|[Er88c], [Er90b]]] ||
@@ Line 31: / Line 31: @@
 |<math>Q_8 \times Q_8</math> || <math>\mathcal{O}</math> || No || [[References#E|[EL20]]] ||
 |-
-|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>
+|Generalised quaternion <math>2</math>-groups || <math>\mathcal{O}</math> || No || [[References#E|[Er88a], [Er88b], [Ei16], [EEKLS26]]] ||
 |-
 |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 noncyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References#C|[CG12]]], [[References#S|[Sa12b]]] || All blocks nilpotent
 |-
 |<math>p_+^{1+2}</math> for <math>p \geq 5</math> || <math>\mathcal{O}</math> || No || [[References#A|[AE23]]] ||

@@ 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 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.
 {| class="wikitable"