# MNA(2,1)

Revision as of 08:03, 24 November 2018 by Charles Eaton (talk | contribs) (Created page with "__NOTITLE__ == Blocks with defect group <math>MNA(2,1)=\langle x,y|x^4=y^2=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle</math> == The defect groups are minimal nonabelian <math>2</...")

## Blocks with defect group [math]MNA(2,1)=\langle x,y|x^4=y^2=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle[/math]

The defect groups are minimal nonabelian [math]2[/math]-groups. The invariants [math]k(B)[/math], [math]l(B)[/math] and [math]k_i(B)[/math] for all [math]i[/math] are determined in [Sa11]. The Cartan matrices are also determined up to equivalence of quadratic forms. These results do not rely on the CFSG. The automorphism group of [math]MNA(2,1)[/math] is a [math]2[/math]-group, but there exists at least one non-nilpotent fusion system for blocks with this defect group.