Finite groups with seminormal or abnormal Sylow subgroups

‎Let $G$ be a finite group in which every Sylow subgroup‎ ‎is seminormal or abnormal‎. ‎We prove that $G$ has a Sylow tower‎. ‎We establish that if a group has a maximal subgroup ‎‎‎‎with Sylow subgroups under the same conditions‎, ‎then this group is soluble‎.

Keywords:

Finite group , Sylow subgroup , abnormal subgroup , seminormal subgroup