Author/Authors :
Alavi, Hassan Department of Mathematics - Bu-Ali Sina University, Hamedan, Iran , Daneshkhah, Ashraf Department of Mathematics - Bu-Ali Sina University, Hamedan, Iran , Parvizi Mosaed, Hosein Alvand Institute of Higher Education, Hamedan, Iran
Abstract :
Abstract. For a nite group G and a positive integer n, let G(n) be the set of all elements in G
such that xn = 1. The groups G and H are said to be of the same (order) type if jG(n)j = jH(n)j,
for all n. The main aim of this paper is to show that if G is a nite group of the same type as Suzuki
groups Sz(q), where q = 22m+1 8, then G is isomorphic to Sz(q). This addresses to the well-known
J. G. Thompson's problem (1987) for simple groups.
