A Characterization of Projective Special Unitary Group PSU(3,3) and Projective Special Linear Group PSL(3,3) by NSE

Abstract

Let G be a finite group and ω(G) be the set of element orders of G. Let k ∈ ω(G) and m k be the number of elements of order k in G. Let nse(G) = {m k |k ∈ ω(G)}. In this paper, we prove that if G is a finite group such that nse(G) = nse(H), where H = PSU(3, 3) or PSL(3, 3), then G ∼ = H.Keywords: element order; number of elements of the same order; projective special linear group; projective special unitary group; simple K n -group

A Characterization of U4(2) by Nse

“…Besides, in [1,14,15,16] it is proved that U 3 (4), L 3 (4), U 3 (5), L 3 (5), are uniquely determined by nse(G). Recently, in [3,6,18,19], it is proved that the simple groups In an effort to fill some of the empty ground about the characterization of simple groups by nse, in this paper we will prove the following main theorem. Main Theorem.…”