NSE characterization of some Suzuki groups

چکیده مقاله

Let G be a group, and π_e(G) be the set of element orders of G. For k ϵ π_e(G), the number of elements of G of order k is denoted by m_k (G). Set nse(G) = {m_k (G) | k ϵ π_e(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 π_e(G) but p² ∉ π_e(G), then G≅= Sz(q) or G≅= Sz(q) ⋊ ℤ_2n+1. © 2019, Institute of Mathematics, Academy of Sciences Moldova. All rights reserved.