Finite Groups and the Sum of Orders of Their Subgroups

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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 $G= A_5.$

Keywords:

Finite groups Solvable groups subgroup orders.
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DOI

10.4208/jms.v56n4.23.02

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