%0 Journal Article
%T A Characterization of the Small Suzuki Groups by the Number of the Same Element Order
%J Journal of Sciences, Islamic Republic of Iran
%I University of Tehran
%Z 1016-1104
%A Parvizi Mosaed, H.
%A Iranmanesh, A.
%A Tehranian, A.
%D 2015
%\ 06/01/2015
%V 26
%N 2
%P 171-177
%! A Characterization of the Small Suzuki Groups by the Number of the Same Element Order
%K Element order
%K Sylow subgroup
%K Simple -group
%K Suzuki group
%R
%X 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.
%U https://jsciences.ut.ac.ir/article_54649_b9016d7ddd6b44de3979a6084b8ac13e.pdf