TY - JOUR ID - 17196 TI - A characterization of the Suzuki group Sz(2^9) by the set of the number of elements with the same order JO - Journal of Advanced Mathematical Modeling JA - JAMM LA - en SN - 2251-8088 AU - Parvizi Mosaed, Hosein AU - Deneshkhah, Ashraf AU - Alavi, Seyed Hassan AD - Alvand Institute of Higher Education, Hamedan, Iran AD - Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran Y1 - 1400 PY - 1400 VL - 11 IS - 4 SP - 679 EP - 685 KW - Finite simple group KW - Suzuki group KW - Element order KW - Prime graph DO - 10.22055/jamm.2021.38473.1961 N2 - 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 ). UR - https://jamm.scu.ac.ir/article_17196.html L1 - https://jamm.scu.ac.ir/article_17196_46dbbeb39a67106f317d13188938f5db.pdf ER -