Khmelnytskyi M. Groups with the weak pi-minimality and the weak pi-maximality conditions

Locally nilpotent and periodic almost solvable groups with weak pi- and pi-layer minimality conditions and pi- and pi-layer maximality conditions are investigated. Necessary and sufficient conditions for a locally nilpotent group to satisfy the weak pi- and pi-layer minimality conditions and pi- and pi-layer maximality conditions are obtained. Also necessary and sufficient conditions for a periodic almost solvable group to satisfy the weak pi- and pi-layer minimality conditions and pi- and pi-layer maximality conditions are obtained. Description of groups possessing the ascending normal series with the locally nilpotent and locally finite factors which satisfy the weak pi-maximality condition and contain the infinite normal pi-subgroup is obtained.