A Characterization of the Small Suzuki Groups by the Number of the Same Element Order
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Tehran
2015-06-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Subjects: | |
| Online Access: | https://jsciences.ut.ac.ir/article_54649_b9016d7ddd6b44de3979a6084b8ac13e.pdf |
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| Summary: | 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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| ISSN: | 1016-1104 2345-6914 |