A Characterization of the Small Suzuki Groups by the Number of the Same Element Order
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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.
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Journal title
volume 26 issue 2
pages 171- 177
publication date 2015-06-01
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