Volume 56, Issue 4
Finite Groups and the Sum of Orders of Their Subgroups

Jiakuan Lu, Meiqun Kuang, Kaixun Wu & Boru Zhang

J. Math. Study, 56 (2023), pp. 340-344.

Published online: 2023-12

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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 $G= A_5.$

  • AMS Subject Headings

20D60, 20D10

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COPYRIGHT: © Global Science Press

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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 $G= A_5.$

Lu , JiakuanKuang , MeiqunWu , Kaixun and Zhang , Boru. (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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