- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 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 :