Mathematica Eterna
Open Access

Abstract

A new characterization of L2(2m) by nse

Yong Yang and Haiyan Zhan

Let G be a group and ω(G) be the set of element orders of G. Let k ∈ ω(G) and sk be the number of elements of order k in G. Let nse(G) = {sk k ∈ ω(G)}. The groups L2(8) and L2(16) are unique determined by nse(G). In this paper, we prove that if G is a group such that nse(G)=nse(L2(2m)), then G ∼= L2(2m).