Finite Groups and the Sum of Orders of Their Subgroups (Journal of Mathematical Study, 2023)
Let $G$ be a finite group and $σ_1(G) = \frac{1}{|G|} ∑_{H≤G} |H|.$ In this paper, we provethat if $G$ is a nonsolvable group and $σ_1(G)=\frac{117}{ 20},$ then $G= A_5.$
Keywords: Finite groups; Solvable groups; subgroup orders.