Status of Donovan's conjecture
In this page we list cases where Donovan's conjecture is known to hold. The first list is organised by [math]p[/math]-group, and the second by class of finite groups.
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Donovan's conjecture by [math]p[/math]-group
[math]p[/math]-groups | Donovan's conjecture | Puig's conjecture | References | Notes |
---|---|---|---|---|
Cyclic [math]p[/math]-groups | [math]\mathcal{O}[/math] | Yes | ||
[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]k[/math] | No | ||
[math]C_3 \times C_3[/math] | No | No | [Ko03] | Puig's conjecture known for principal blocks |
Dihedral [math]2[/math]-groups | [math]k[/math] | No | [Er90]] | |
Semidihedral [math]2[/math]-groups | [math]k[/math] | No | [Er90]] | |
Generalised quaternion [math]2[/math]-groups | No | No | [Er90]] | 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 |