Document Type : Original Paper

Authors

• H. Parvizi Mosaed ¹
• A. Iranmanesh ²
• A. Tehranian ¹

¹ 1Department of Mathematics, Faculty of Basic Sciences, Science and Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran

² 2Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran

Abstract

Suppose that  is a finite group. Then the set of all prime divisors of  is denoted by  and the set of element orders of  is denoted by . Suppose that . Then the number of elements of order  in  is denoted by  and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if  is a group such that , where , then . Here  denotes the family of Suzuki simple groups, , . This proves that the second and third member of the family of Suzuki simple groups are characterizable by the set of the number of the same element order.

Keywords

• Element order
• Sylow subgroup
• Simple -group
• Suzuki group