A Characterization of the Small Suzuki Groups by the Number of the Same Element Order - H. Parvizi Mosaed; A. Iranmanesh; A. Tehranian (Journal of Sciences, Islamic Republic of Iran)
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.