TY - JOUR
T1 - Finite Groups and the Sum of Orders of Their Subgroups
AU - Lu , Jiakuan
AU - Kuang , Meiqun
AU - Wu , Kaixun
AU - Zhang , Boru
JO - Journal of Mathematical Study
VL - 4
SP - 340
EP - 344
PY - 2023
DA - 2023/12
SN - 56
DO - http://doi.org/10.4208/jms.v56n4.23.02
UR - https://global-sci.org/intro/article_detail/jms/22253.html
KW - Finite groups, Solvable groups, subgroup orders.
AB - <p style="text-align: justify;">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 $G= A_5.$</p>