A new characterization of L 2 (2 m ) by nse

Yong Yang, Haiyan Zhang
2014 Mathematica Aeterna   unpublished
Let G be a group and ω(G) be the set of element orders of G. Let k ∈ ω(G) and s k be the number of elements of order k in G. Let nse(G) = {s k k ∈ ω(G)}. The groups L 2 (8) and L 2 (16) are unique determined by nse(G). In this paper, we prove that if G is a group such that nse(G)=nse(L 2 (2 m)), then G ∼ = L 2 (2 m). Mathematics Subject Classification: 20D05, 20D06, 20D20.