Finite Groups and the Sum of Orders of Their Subgroups
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@Article{JMS-56-340,
author = {Lu , JiakuanKuang , MeiqunWu , 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 = {http://global-sci.org/intro/article_detail/jms/22253.html} }
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 -
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 $G= A_5.$
Jiakuan Lu, Meiqun Kuang, Kaixun Wu & Boru Zhang. (2023). Finite Groups and the Sum of Orders of Their Subgroups.
Journal of Mathematical Study. 56 (4).
340-344.
doi:10.4208/jms.v56n4.23.02
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