Constructing Perfect Groups

Abstract: The construction of perfect groups of a given order can be considered as the prototype of construction of nonsolvable groups of a given order. I will describe a recent project to enumerate, up to isomorphism, the perfect groups of order up to 2*10^6. It crucially relies on new tools for calculating cohmology, as well as improved implementations for isomorphism test.

This work extends results of Holt and Plesken from 1989 and illustrates the scope of algorithmic improvements over the past decades.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle