On the solvability of a finite group by the sum of subgroup orders
Bull. Korean Math. Soc.
Published online September 3, 2020
MARIUS TARNAUCEANU
FACULTY OF MATHEMATICS, AL. I. CUZA UNIVERSITY OF IASI, ROMANIA
Abstract : Let $G$ be a finite group and $\sigma_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of $G$, we prove that if $\sigma_1(G)<\frac{117}{20}\,$, then $G$ is solvable. This partially solves an open problem posed in \cite{6}.
Keywords : subgroup orders, solvable groups.
MSC numbers : 20D60; 20D10; 20F16; 20F17.
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd