Universal deformation rings for extensions of finite subgoups of $G{l}_2(\mathbb{C})$

Abstract

In this paper we expand on previous results, studying the extent to which one can detect fusion in certain finite groups $\Gamma$, from information about the universal deformation rings of absolutely irreducible ${\mathbb{F}}_p\Gamma$-modules. We consider groups which are extensions of finite irreducible subgroups of $G{l}_2(\mathbb{C})$ by elementary abelian $p$-groups of rank $2$.