MNA(3,1):C2
Revision as of 14:58, 12 April 2019 by Charles Eaton (talk | contribs) (Created page with "__NOTITLE__ == Blocks with defect group <math>MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle</math> == Sambale h...")
Blocks with defect group [math]MNA(3,1):C_2=\langle a,b,c,d | a^2=b^2=c^2=d^4=1, ab=ba, ac=ca, dad^{-1}=abc, dbd^{-1}=bc=cb, cd=dc \rangle[/math]
Sambale has used GAP to show that there are no non-trivial saturated fusion systems on [math]MNA(3,1):C_2[/math] (see [Sa14]). See also [vdW, pp. 382]. Hence every block with this defect group is nilpotent.
There is a unique [math]\mathcal{O}[/math]-Morita equivalence class.
| Class | Representative | # lifts / [math]\mathcal{O}[/math] | [math]k(B)[/math] | [math]l(B)[/math] | Inertial quotients | [math]{\rm Pic}_\mathcal{O}(B)[/math] | [math]{\rm Pic}_k(B)[/math] | [math]{\rm mf_\mathcal{O}(B)}[/math] | [math]{\rm mf_k(B)}[/math] | Notes |
|---|---|---|---|---|---|---|---|---|---|---|
| M(32,4,1) | [math]k(MNA(3,1):C_2)[/math] | 1 | 11 (8,2,1) | 1 | [math]1[/math] | 1 | 1 |
