(untitled) (Communications in Mathematical Research, 2021)
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)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.