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A new characterization of alternating and symmetric groups

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Abstract

In this paper we prove that the alternating groupsA n , forn=p, p+1, p+2 and symmetric groupsS n , forn=p, p+1, wherep>=3 is a prime number, can be uniquely determined by their order components. As one of the important consequence of this characterization we show that the simple groupsA n , wheren=p, p+1, p+2 andp>=3 is prime, satisfy in Thompson's conjecture and Shi's conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Bu-Ali Sina University, P. O. Box: 65174-4111, Hamadan, Iran

    S. H. Alavi & A. Daneshkhah

Authors
  1. S. H. Alavi
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  2. A. Daneshkhah
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Correspondence to A. Daneshkhah.

Additional information

A. Daneshkhah received her B. Sc., M. Sc. and Ph. D. degrees from the Tehran University, Tehran, Iran, in 1994 under the supervision of professor M. R. Darafsheh. Since 1994 she has been employed at Bu-Ali Sina University as an assistant professor. Her research interests center on representation and character theory of finite groups, quasi permutation representation of finite groups and characterization of finite groups.

S. H. Alavi recieved his B. Sc. degree from B-Ali Sina University in 1998. In 2001, he obtained his M. Sc. degree from the university of Tarbiat Modarres under the supervision of Prof. A. Iranmanesh. His research interests center on character theory of finite groups and characterization of finite groups.

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Alavi, S.H., Daneshkhah, A. A new characterization of alternating and symmetric groups. JAMC 17, 245–258 (2005). https://doi.org/10.1007/BF02936052

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