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Algebra and Discrete Mathematics, 2014, Volume 18, Issue 1, Pages 8–13
(Mi adm477)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 15.01.2014 Revised: 14.02.2014
Citation:
Alireza Khalili Asboei, Syyed Sadegh Salehi Amiri, Ali Iranmanesh, “A new characterization of alternating groups”, Algebra Discrete Math., 18:1 (2014), 8–13
Linking options:
https://www.mathnet.ru/eng/adm477 https://www.mathnet.ru/eng/adm/v18/i1/p8
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