A characterization of the Suzuki group Sz(2^9) by the set of the number of elements with the same order

Document Type : Original Paper


1 Alvand Institute of Higher Education, Hamedan, Iran

2 Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran


Let G be a group, and let nse(G) be the set of the number of elements with the same order in group G. In this paper, we prove that if G is a group and Sz(2^9) is the Suzuki simple group such that nse(G) = nse(Sz(2^9)), then G is isomorphic to the Suzuki simple group Sz(2^9). In other words, we prove that the simple Suzuki group Sz(2^9) is uniquely determined by its set of the number of elements with the same order. Consequently, Thompson’s problem is true for the Suzuki simple group Sz(2^9 ).


Main Subjects

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