A new characterization of symmetric groups for some

Abstract

Let G be a finite group and let πe(G) be the set of element orders G.Let k ∈ πe(G) and let mk be the number of elements of order k in G.Set nse(G):={mk|k ∈ πe(G)}. In this paper, we prove that if G is agroup such that nse(G)=nse(Sn) where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.2000 AMS Classification: 20D60, 20D06