On faithful quasi-permutation representations of VZ-groups and Camina p-groups

Abstract

For a finite group G, we denote by µ(G), and c(G), the minimal degree of faithful permutation representation of G, and the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C, respectively. In this article, we study µ(G), and c(G) for various classes of finite non-abelian p-groups with cyclic center. We prove a result for normally monomial p-groups with cyclic center which generalizes a result of Behravesh for finite p-groups of class 2 with cyclic center [5, Theorem 4.12]. We also compute minimal degrees for some classes of metabelian p-groups.