NSE characterization of some Suzuki groups

Abstract

Let G be a group, and πe(G) be the set of element orders of G. For k ϵ πe(G), the number of elements of G of order k is denoted by mk (G). Set nse(G) = {mk (G) | k ϵ πe(G)}. Let q = 22n+1, and p = q-1 be a Mersenne prime. In this paper, we show that if G is a group such that nse(G) = nse(Sz(q)) and p ϵ πe(G) but p2 ∉ πe(G), then G≅= Sz(q) or G≅= Sz(q) ⋊ ℤ2n+1. © 2019, Institute of Mathematics, Academy of Sciences Moldova. All rights reserved.