A criterion for $p$-solvability of finite groups, where $p=7$ or $11$

Document Type : Research Paper

Author

Department of Mathematics, Payamenoor University, Tehran, Iran

Abstract

For a finite group $G$, define $ \psi^{\prime \prime}(G)=\psi(G)/|G|^2 $, where $\psi(G)=\sum_{g\in G}o(g)$ and $o(g)$ denotes the order of $g \in G $.  In this paper, we give a criterion for $p$-solvability by the function  $\psi''$, where $ p \in \{7,  11\} $. We prove that if $ G $ is a  finite group and $\psi''(G)>\psi''({\rm PSL}(2, p))$, where $p \in \{7, 11\}$, then $G$ is a $p$-solvable group.

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References

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History

  • Receive Date: 08 August 2023
  • Revise Date: 26 December 2023
  • Accept Date: 28 January 2024

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