Difference between revisions of "Status of Donovan's conjecture"
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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 | ||
|- | |- | ||
| − | |Abelian <math>2</math>-groups || <math> | + | |Abelian <math>2</math>-groups || <math>\mathcal{O}</math> || No || [[References|[EEL18]]] || |
|- | |- | ||
| − | |<math> | + | |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]]] || | ||
| + | |- | ||
| + | |<math>Q_8</math> || <math>\mathcal{O}</math> || No || [[References|[Er88a], [Er88b], [HKL07], [Ei16]]] || | ||
|- | |- | ||
|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
In this page we list cases where Donovan's conjecture is known to hold.
Donovan's conjecture by [math]p[/math]-group
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 |
