Computation of isomorphism classes of 𝑝-groups

Abstract

p p -groups may be classified by splitting the groups up into classes having the same commutator relations (isoclinism classes) and then determining the nonisomorphic groups in each class. This paper reduces the problem of determining the isomorphism classes to that of finding the equivalence classes of a set of matrices under some equivalence relation. A computer is used to find the equivalence classes for the first few values of p p , and these are then used as a guide for finding the solution for general p p .