A NEW CHARACTERIZATION OF SOME LINEAR GROUPS BY NSE

Abstract

Let G be a finite group and π e (G) be the set of element orders of G. Assume that k ∈ π e (G) and m k (G) is the number of elements of order k in G. Set nse (G) ≔ {m k (G) | k ∈ π e (G)}, we call nse (G) the set of numbers of elements with same order. In this paper, we give a new characterization of simple linear group L 2 (2 a ) by its order |L 2 (2 a )| and the set nse (L 2 (2 a )), where either 2 a - 1 or 2 a + 1 is a prime.