Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 427–437

A new characterization of symmetric group by NSE

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Abstract

Let G be a group and ω(G) be the set of element orders of G. Let kω(G) and mk(G) be the number of elements of order k in G. Let nse(G) = {mk(G): kω(G)}. Assume r is a prime number and let G be a group such that nse(G) = nse(Sr), where Sr is the symmetric group of degree r. In this paper we prove that GSr, if r divides the order of G and r2 does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.

Keywords

set of the numbers of elements of the same order prime graph 

MSC 2010

20D06 20D15 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of QomQomIran
  2. 2.Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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