Finite groups with given systems of K-U-subnormal subgroups - Kovaleva, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
A subgroup H of a finite group G is called U-subnormal in Kegel’s sense or K-U-subnormal in G if there exists a chain of subgroups H = H_0 ≤ H_1 ≤ . . . ≤ H_t = G such that either H_i-1 is normal in H_i or H_i/(H_i-1)H_i is supersoluble for any i = 1, . . . , t. We describe finite groups for which every 2-maximal or every 3-maximal subgroup is K-U-subnormal.