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

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PARVIZI MOSAED H.; IRANMANESH A.; TEHRANIAN A.

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ISSN: 2588-4824

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Journal: Journal of Sciences, Islamic Republic of Iran Year:2015 | Volume:26 | Issue:2 Page(s): 171-177

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Title

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

Author(s)

PARVIZI MOSAED H. | IRANMANESH A. | TEHRANIAN A. | Issue Writer Certificate

Keywords

Element order

Sylow subgroup

Simple n K-group

Suzuki group

Abstract

Suppose that G is a finite group. Then the set of all prime divisors of G is denoted by  (G) and the set of Element orders of G is denoted by ( ) e  G. Suppose that ( ) e k   G. Then the number of elements of order k in G is denoted by k m and the sizes of the set of elements with the same order is denoted by nse  G ; that is,    : ( ) k e nse G  m k   G. In this paper, we prove that if G is a group such that nse  G  nse(Sz(n)), where n  32, 128 , then G  Sz(n). Here Sz(n) denotes the family of Suzuki simple groups, n  22k 1, k   . 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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APA: Copy

PARVIZI MOSAED, H., IRANMANESH, A., & TEHRANIAN, A.. (2015). A Characterization of the Small Suzuki Groups by the Number of the Same Element Order. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 26(2), 171-177. SID. https://sid.ir/paper/729456/en

Vancouver: Copy

PARVIZI MOSAED H., IRANMANESH A., TEHRANIAN A.. A Characterization of the Small Suzuki Groups by the Number of the Same Element Order. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2015;26(2):171-177. Available from: https://sid.ir/paper/729456/en

IEEE: Copy

H. PARVIZI MOSAED, A. IRANMANESH, and A. TEHRANIAN, “A Characterization of the Small Suzuki Groups by the Number of the Same Element Order,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 26, no. 2, pp. 171–177, 2015, [Online]. Available: https://sid.ir/paper/729456/en

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