For a finite group G and a positive integer n, let G(n) be the set of all elements in G such that x n = 1. The groups G and H are said to be of the same (order) type if |G(n)| = |H(n)|, for all n. The main aim of this paper is to show that if G is a finite group of the same type as Suzuki groups Sz(q), where q = 2 2m+1 ≥ 8, then G is isomorphic to Sz(q). This addresses to the well-known J. G. Thompson’s problem (1987) for simple groups.
