On Finite Groups Satisfying the Permutizer Condition Original Research Article

A groupGsatisfies thepermutizer conditionPif each proper subgroupHofGpermutes with some cyclic subgroup not contained inH. The structure of finite groups withPis studied, the main result being that such groups are soluble with chief factors of order 4 or a prime. The classification of finite simple groups is used, as is detailed information about maximal factorizations of almost simple groups.