@Article{JMS-56-4, author = {Lu, Jiakuan and Meiqun, Kuang and Wu, Kaixun and Zhang, Boru}, title = {Finite Groups and the Sum of Orders of Their Subgroups}, journal = {Journal of Mathematical Study}, year = {2023}, volume = {56}, number = {4}, pages = {340--344}, 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 $G= A_5.$

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v56n4.23.02}, url = {https://global-sci.com/article/87630/finite-groups-and-the-sum-of-orders-of-their-subgroups} }