Finite Groups and the Sum of Orders of Their Subgroups

Authors

  • Jiakuan Lu
  • Meiqun Kuang
  • Kaixun Wu
  • Boru Zhang

DOI:

https://doi.org/10.4208/jms.v56n4.23.02

Keywords:

Finite groups, Solvable groups, subgroup orders.

Abstract

Let $G$ be a finite group and $σ_1(G) = \frac{1}{|G|} ∑_{H≤G} |H|.$ In this paper, we prove that if $G$ is a nonsolvable group and $σ_1(G)=\frac{117}{ 20},$ then $G= A_5.$

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Published

2023-12-13

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Issue

Vol. 56 No. 4 (2023)

Section

Articles

How to Cite

Finite Groups and the Sum of Orders of Their Subgroups. (2023). Journal of Mathematical Study, 56(4), 340-344. https://doi.org/10.4208/jms.v56n4.23.02