<abstract xmlns="http://www.w3.org/1999/xhtml"> Let G be a finite group and πe(G) be the set of element orders of G. Let k ∈ πe (G)and mk be the number of elements of order k in G. Set nse(G):={mk|k ∈ πe (G)}. It is proved that An are uniquely determined by nse(An), where n ∈ {4,5,6}. In this paper, we prove that if G is a group such that nse(G)=nse(An) where n ∈ {7,8}, then G ≅ An. </abstract>

Let G be a finite group and πe(G) be the set of element orders of G. Let k ∈ πe (G)and mk be the number of elements of order k in G. Set nse(G):={mk|k ∈ πe (G)}. It is proved that An are uniquely determined by nse(An), where n ∈ {4,5,6}. In this paper, we prove that if G is a group such that nse(G)=nse(An) where n ∈ {7,8}, then G ≅ An.

A new characterization of A7 and A8

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Department of Mathematics, Tarbiat Modares University P. O. Box: 14115-137, Tehran, Iran

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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Let G be a finite group and πe(G) be the set of element orders of G. Let k ∈ πe (G)and mk be the number of elements of order k in G. Set nse(G):={mk|k ∈ πe...

A new characterization of A₇ and A₈

Published Online: Mar 05, 2014

Page range: 43 - 50

DOI: https://doi.org/10.2478/auom-2013-0041

Keywords
Element order, set of the numbers of elements of the same order, alternating group

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