Minimal non-abelian groups with an average condition on subgroups

Document Type : Research Paper

Authors

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111‎, ‎Iran

Abstract

For a finite group $G$, the average order   $o(G)$   is defined to be the average of all order elements in $G$. We say that $G$ satisfies the average condition if $o(H)\leq o(G)$ for all subgroups $H$ of $G$. In [On a question of Jaikin-Zapirain about the average order elements of finite groups, Int. J. Group Theory, To appear] we proved that every abelian group satisfies the average condition. In this paper, we classify minimal non-abelian groups which satisfy the average condition.

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References

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Journal of Mahani Mathematical Research
Volume 14, Issue 1 - Serial Number 31
January 2025
Pages 387-397

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History

  • Receive Date: 02 July 2024
  • Revise Date: 17 September 2024
  • Accept Date: 01 November 2024

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