Difference between revisions of "Status of Donovan's conjecture"
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[[Image:Donovan.jpg|150px|thumb|right|Peter Donovan]] | [[Image:Donovan.jpg|150px|thumb|right|Peter Donovan]] | ||
| − | In this page we list cases where Donovan's conjecture is known to hold | + | 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>. | |
{| class="wikitable" | {| class="wikitable" | ||
| Line 15: | Line 15: | ||
! scope="col"| Notes | ! scope="col"| Notes | ||
|- | |- | ||
| − | |Cyclic <math>p</math>-groups || <math>\mathcal{O}</math> || Yes || || | + | |Cyclic <math>p</math>-groups || <math>\mathcal{O}</math> || Yes || [[References|[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 | + | |<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>k</math> || No || || | + | |Abelian <math>2</math>-groups || <math>k</math> || No || [[References|[EL18b]]] || |
|- | |- | ||
|<math>C_3 \times C_3</math> || No || No || [Ko03] || Puig's conjecture known for principal blocks | |<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 || [ | + | |Dihedral <math>2</math>-groups || <math>k</math> || No || [[References|[Er87]]] || |
|- | |- | ||
| − | |Semidihedral <math>2</math>-groups || <math>k</math> || No || [ | + | |Semidihedral <math>2</math>-groups || <math>k</math> || No || [[References|[Er88c], [Er90b]]] || |
|- | |- | ||
| − | |Generalised quaternion <math>2</math>-groups || No || No || [ | + | |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> |
|- | |- | ||
| − | |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 | + | |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 || [[References|[EKS12]]] || Additional assumptions on <math>\mathcal{O}</math>, which may not be necessary |
|} | |} | ||
Revision as of 16:50, 14 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 |
