The Degree of a p-group G with | G' | = p

Abstract

Let G be a finite group and δ (G) denote the least n ∈   such that G is isomorphic to a subgroup of the symmetric group Sn. The number δ (G) is called the degree of G. This paper is a note on δ (G) for a nite p-group G with derived subgroup of order p. Our method is based on quasi- permutation representations of a finite group.