Author/Authors :
Parvizi Mosaed، H. نويسنده Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran , , Tehranian، A. نويسنده , , Iranmanesh، A. نويسنده Department 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.
