Difference between revisions of "Status of Donovan's conjecture"
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== Donovan's conjecture by <math>p</math>-group == | == Donovan's conjecture by <math>p</math>-group == | ||
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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>. | ||
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|Metacyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References|[Sa12b]]] || All blocks nilpotent | |Metacyclic <math>2</math>-groups of nonmaximal class || <math>\mathcal{O}</math> || No || [[References|[Sa12b]]] || All blocks nilpotent | ||
| + | |} | ||
| + | |||
| + | <!-- == Donovan's conjecture by class of group or block == | ||
| + | |||
| + | [[Image:under-construction.png|50px|left]] | ||
| + | |||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | ! scope="col"| Groups/blocks | ||
| + | ! scope="col"| Donovan's conjecture | ||
| + | ! scope="col"| Puig's conjecture | ||
| + | ! scope="col"| References | ||
| + | ! scope="col"| Notes | ||
| + | |- | ||
| + | |<math>p</math>-solvable groups || <math>\mathcal{O}</math> || Yes || Over <math>k</math> by [[References|[Ku81]]], Puig's conjecture by [[References|[Pu09]]] || See [[References|[Li18d,10.6.2]]] | ||
| + | |- | ||
| + | |Symmetric groups || --> | ||
|} | |} | ||
Revision as of 10:09, 13 October 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] | |
| [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] | |
| Metacyclic [math]2[/math]-groups of nonmaximal class | [math]\mathcal{O}[/math] | No | [Sa12b] | All blocks nilpotent |
|}
