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