On Quasinormal Subgroups II

W. E. Deskins
1966 Nagoya mathematical journal  
A subgroup was defined by O. Ore to be quasinormal in a group if it permuted with all subgroups of the group, and he proved [5] that such a subgroup is subnormal (= subinvariant = accessible) in a finite group. Finite groups in which all subgroups are quasinormal were classified by K. Iwasawa [3], and more recently N. Ito and J. Szép [2] and the author [1] proved that a quasi-normal subgroup is an extension of a normal subgroup by a nilpotent group. Similar results were obtained by O. Kegel [4]
more » ... and in [1] for subgroups which permute not necessarily with all subgroups but with those having some special property.
doi:10.1017/s0027763000012034 fatcat:z6d5cvqkyjeh3lbslntgq27ukq