%0 Journal Article
%T A characterization of the Suzuki group Sz(2^9) by the set of the number of elements with the same order
%J Journal of Advanced Mathematical Modeling
%I Shahid Chamran University of Ahvaz
%Z 2251-8088
%A Parvizi Mosaed, Hosein
%A Deneshkhah, Ashraf
%A Alavi, Seyed Hassan
%D 1400
%\ 10/01/1400
%V 11
%N 4
%P 679-685
%! A characterization of the Suzuki group Sz(2^9) by the set of the number of elements with the same order
%K Finite simple group
%K Suzuki group
%K Element order
%K Prime graph
%R 10.22055/jamm.2021.38473.1961
%X 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, Thompsonâ€™s problem is true for the Suzuki simple group Sz(2^9 ).
%U https://jamm.scu.ac.ir/article_17196_46dbbeb39a67106f317d13188938f5db.pdf