Quasi-permutation representations of some minimal non-abelian q-groups

Abstract

In [1], c(G), q(G) and p(G) are defined for a finite group G.  In this paper, we will calculate c(G), q(G) and p(G) for the following minimal non abelian p-groups:

     G = { a, b | a^{\(p^m\)} = b^p = c^p = 1, [a, b] = c, [a, c] = [b, c] =  1 },

and will show that

     c(G) = q(G) = p(G) = p c(Z(G)) = p^m + p² .