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 Algebra Discrete Math., 2014, Volume 18, Issue 1, Pages 8–13 (Mi adm477)  RESEARCH ARTICLE

A new characterization of alternating groups

Alireza Khalili Asboeiab, Syyed Sadegh Salehi Amiric, Ali Iranmaneshd

a Department of Mathematics, College of Engineering, Buin Zahra Branch, Islamic Azad University, Buin Zahra, Iran
b Department of Mathematics, Farhangian University, Shariati Mazandaran, Iran
c Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran
d Department of Mathematics, Tarbiat Modares University P. O. Box: 14115-137, Tehran, Iran

Abstract: Let $G$ be a finite group and let $\pi_{e}(G)$ be the set of element orders of $G$. Let $k \in \pi_{e}(G)$ and let $m_{k}$ be the number of elements of order $k$ in $G$. Set $\mathrm{nse}(G):=\{ m_{k} | k \in \pi_{e}(G)\}$. In this paper, we show that if $n = r$, $r +1$, $r + 2$, $r + 3$ $r+4$, or $r + 5$ where $r\geq5$ is the greatest prime not exceeding $n$, then $A_{n}$ characterizable by nse and order.

Keywords: finite group, simple group, alternating groups. Full text: PDF file (287 kB) References: PDF file   HTML file

Bibliographic databases: MSC: 20D06, 20D60
Revised: 14.02.2014
Language:

Citation: Alireza Khalili Asboei, Syyed Sadegh Salehi Amiri, Ali Iranmanesh, “A new characterization of alternating groups”, Algebra Discrete Math., 18:1 (2014), 8–13 Citation in format AMSBIB
\Bibitem{AsbAmiIra14} \by Alireza~Khalili~Asboei, Syyed~Sadegh~Salehi~Amiri, Ali~Iranmanesh \paper A new characterization of alternating groups \jour Algebra Discrete Math. \yr 2014 \vol 18 \issue 1 \pages 8--13 \mathnet{http://mi.mathnet.ru/adm477} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3280252} 

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This publication is cited in the following articles:
1. A. K. Asboei, S. S. S. Amiri, A. Iranmanesh, “A new characterization of $\mathrm{PSL}(2,q)$ for some $q$”, Ukr. Math. J., 67:9 (2016), 1297–1305     •  Contact us: math-net2020_04 [at] mi-ras ru Terms of Use Registration Logotypes © Steklov Mathematical Institute RAS, 2020