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Recognition by the Product Element Orders

  • Behrooz KhosraviEmail author
  • Morteza Baniasad Azad
Article
  • 9 Downloads

Abstract

Let G be a finite group. Let \(\psi ^{\prime }(G)= \prod _{g \in G} o(g), \) where o(g) denotes the order of \(g \in G\). In this paper, we prove that \(\mathrm{PSL}(2, 7)\) and \(\mathrm{PSL}(2, 11)\) are uniquely determined by their product of element orders. Furthermore, we prove that \(\mathrm{PSL}(2, 5)\) and \(\mathrm{PSL}(2, 13)\) are uniquely determined by their orders and the product of element orders.

Keywords

Finite groups Simple group Element orders Product of element orders 

Mathematics Subject Classification

20D60 

Notes

Acknowledgements

The authors would like to express their appreciation to the anonymous referees for their constructive remarks and useful suggestions.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of Pure Mathematics, Faculty of Mathematics and Computer ScienceAmirkabir University of Technology (Tehran Polytechnic)TehranIran

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