A new characterization of Suzuki groups

Abstract

One of the important questions that remains after the classification of the finite simple groups is how to recognize a simple group via specific properties. For example, authors have been able to use graphs associated to element orders and to number of elements with specific orders to determine simple groups up to isomorphism. In this paper, we prove that Suzuki groups Sz(q), where q ± √ 2q + 1 is a prime number can be uniquely determined by the order of group and the number of elements with the same order.