A Characterization of the Small Suzuki Groups by the Number of the Same Element Order

نویسندگان

  • A. Iranmanesh 2Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran
  • A. Tehranian 1Department of Mathematics, Faculty of Basic Sciences, Science and Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran
  • H. Parvizi Mosaed 1Department of Mathematics, Faculty of Basic Sciences, Science and Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran
چکیده مقاله:

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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a characterization of the small suzuki groups by the number of the same element order

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عنوان ژورنال

دوره 26  شماره 2

صفحات  171- 177

تاریخ انتشار 2015-06-01

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