A new characterization of PSL(2, 27)

Abstract

Let G be a finite group and pi_{e}(G) be the set of element orders of G. Let k in pi_{e}(G)$ and m_{k} be the number of elements of order k in G. Set nse(G):={ m_{k} | k in pi_{e}(G)}. In this paper, we prove that if G is a group such that nse(G)=nse(PSL(2, 27)) then G is isomophic to PSL(2, 27).

Keywords

• Element order
• set of the numbers of elements of the same