Sub-Cover-Avoidance Properties and the Structure of Finite Groups

Abstract

A subgroup $H$ of a group $G$ is said to have the sub-cover-avoidance property in $G$ if there is a chief series $1 = G_0 ≤ G_1 ≤ · · · ≤ G_n = G$, such that $G_{i−1}(H ∩ G_i)\lhd \lhd G$ for every $i = 1, 2, · · · , l$. In this paper, we give some characteristic conditions for a group to be solvable under the assumptions that some subgroups of a group satisfy the sub-cover-avoidance property.