Difference between revisions of "Status of Donovan's conjecture"
(→Donovan's conjecture by p-group) |
|||
Line 4: | Line 4: | ||
== Donovan's conjecture by <math>p</math>-group == | == Donovan's conjecture by <math>p</math>-group == | ||
+ | |||
+ | [[Image:under-construction.png|50px|left]] | ||
In the following, the column headed Donovan's conjecture indicates whether the conjecture is known over <math>k</math> or <math>\mathcal{O}</math>. | In the following, the column headed Donovan's conjecture indicates whether the conjecture is known over <math>k</math> or <math>\mathcal{O}</math>. |
Revision as of 15:25, 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]k[/math] | No | [EL18b] | |
[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 | [Er87] | |
Semidihedral [math]2[/math]-groups | [math]k[/math] | No | [Er88c], [Er90b] | |
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 |