Difference between revisions of "Status of Donovan's conjecture"

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(Donovan's conjecture by p-group)
([EEL18])
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|<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|[CEKL11]]] || Donovan's conjecture without CFSG, Puig using CFSG
 
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|Abelian <math>2</math>-groups || <math>k</math> || No || [[References|[EL18b]]] ||
+
|Abelian <math>2</math>-groups || <math>\mathcal{O}</math> || No || [[References|[EEL18]]] ||
 
|-
 
|-
|<math>C_3 \times C_3</math> || No || No || [Ko03] || Puig's conjecture known for principal blocks
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|Abelian <math>3</math>-groups || No || No || [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|[Er87]]] ||
 
|-
 
|-
 
|Semidihedral <math>2</math>-groups || <math>k</math> || No || [[References|[Er88c], [Er90b]]] ||
 
|Semidihedral <math>2</math>-groups || <math>k</math> || No || [[References|[Er88c], [Er90b]]] ||
 +
|-
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|<math>Q_8</math> || <math>\mathcal{O}</math> || No || [[References|[Er88a], [Er88b], [HKL07], [Ei16]]] ||
 
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|-
 
|Generalised quaternion <math>2</math>-groups || No || No || [[References|[Er88a], [Er88b]]] || Donovan's conjecture over <math>k</math> known if <math>l(B) \neq 2</math>
 
|Generalised quaternion <math>2</math>-groups || No || No || [[References|[Er88a], [Er88b]]] || Donovan's conjecture over <math>k</math> known if <math>l(B) \neq 2</math>

Revision as of 21:44, 26 September 2018

Peter Donovan

In this page we list cases where Donovan's conjecture is known to hold.

Donovan's conjecture by [math]p[/math]-group

Under-construction.png

In the following, the column headed Donovan's conjecture indicates whether the conjecture is known over [math]k[/math] or [math]\mathcal{O}[/math].

[math]p[/math]-groups Donovan's conjecture Puig's conjecture References Notes
Cyclic [math]p[/math]-groups [math]\mathcal{O}[/math] Yes [Li96]
Abelian [math]2[/math]-groups [math]P[/math] such that [math]{\rm Aut}(P)[/math] is a [math]2[/math]-group [math]\mathcal{O}[/math] Yes All blocks are nilpotent
[math]C_2 \times C_2[/math] [math]\mathcal{O}[/math] Yes [CEKL11] Donovan's conjecture without CFSG, Puig using CFSG
Abelian [math]2[/math]-groups [math]\mathcal{O}[/math] No [EEL18]
Abelian [math]3[/math]-groups No No [Ko03] Puig's conjecture known for principal blocks
Dihedral [math]2[/math]-groups [math]k[/math] No [Er87]
Semidihedral [math]2[/math]-groups [math]k[/math] No [Er88c], [Er90b]
[math]Q_8[/math] [math]\mathcal{O}[/math] No [Er88a], [Er88b], [HKL07], [Ei16]
Generalised quaternion [math]2[/math]-groups No No [Er88a], [Er88b] Donovan's conjecture over [math]k[/math] known if [math]l(B) \neq 2[/math]
Minimal nonabelian [math]2[/math]-groups [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 [EKS12] Additional assumptions on [math]\mathcal{O}[/math], which may not be necessary