A new criterion for solvability of a finite group by the sum of orders of non-normal subgroups
Volume 174 / 2023
Colloquium Mathematicum 174 (2023), 169-176
MSC: Primary 20D10; Secondary 20D20.
DOI: 10.4064/cm9175-10-2023
Published online: 30 October 2023
Abstract
Let $G$ be a finite group and $\nu _0(G)=\frac {1}{|G|}\sum _{H\leq G,\, H\not \unlhd G}|H|$. We prove that $G$ is solvable if $\nu _0(G) \lt {29}/{6}$.
