Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808811414001001A characterization of the Suzuki group Sz(2^9) by the set of the number of elements with the same orderA characterization of the Suzuki group Sz(2^9) by the set of the number of elements with the same order6796851719610.22055/jamm.2021.38473.1961FAHoseinParvizi MosaedAlvand Institute of Higher Education, Hamedan, IranAshrafDeneshkhahDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranSeyed HassanAlaviDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranJournal Article14000614Let 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 ).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 ).https://jamm.scu.ac.ir/article_17196_46dbbeb39a67106f317d13188938f5db.pdf