On nonnilpotent groups in which every two 3-maximal subgroups are permutable

Abstract

We describe the structure of finite nonnilpotent groups in which every two 3-maximal subgroups are permutable. In particular, we describe finite nonnilpotent groups in which all 2-maximal or all 3-maximal subgroups are normal.

Finite groups with all 3-maximal subgroups K-U-subnormal

“…Skiba described the groups whose every 3-maximal subgroup permutes with all maximal subgroups. In [19], W. Guo, Yu.V. Lutsenko and A.N.…”

On $n$-maximal subgroups of finite groups

“…Description was obtained in [10] of groups whose every 3-maximal subgroup permutes with all maximal subgroups. The nonnilpotent groups are described in [11] in which every two 3-maximal subgroups are permutable. The groups are described in [12] whose all 3-maximal subgroups are S-quasinormal, that is, permute with all Sylow subgroups.…”