Sub-Cover-Avoidance Properties and the Structure of Finite Groups (Communications in Mathematical Research, 2021)
A subgroup $H$ of a group $G$ is said to have the sub-cover-avoidanceproperty in $G$ if there is a chief series $1 = G_0 ≤ G_1 ≤ · · · ≤ G_n = G$, suchthat $G_{i−1}(H ∩ G_i)\lhd \lhd G$ for every $i = 1, 2, · · · , l$. In this paper, we give somecharacteristic conditions for a group to be solvable under the assumptions that somesubgroups of a group satisfy the sub-cover-avoidance property.