Groups in which every Strongly 3-maximal subgroup permutes with all maximal subgroups
Yuliya V. Gorbatova, O V Kubanskikh · Herald of Omsk University · 2023
The description of the structure of finite non-nilpotent groups in which every strongly 3-maximal subgroup permutes with all maximal subgroups is the main result of this paper.In particular, we prove that the groups with the noted property are solvable and their structure is equivalent to the structure of groups in which every maximal subgroup permutes with all 3-maximal subgroups.The obtained results also prove the nilpotency of a finite group in which every strongly 3-maximal subgroup permutes with all maximal subgroupsif the number of prime divisors of the order of this group is not less than 4.