Drushlyak M. Groups with the restrictions on given systems of subgroups

Thesis is devoted to the research of properties and structure of groups with restrictions on $sigma$-norms, which are intersection of normalizers of all subgroups of the unempty system with certain theoretical-group property. The non-Dedekindness of $sigma$-norm gets out as determining restriction, and the system of all Abelian non-cyclic subgroups and the system of all cyclic subgroups of non-prime orders get out as a system $sigma$. Such $sigma$ -norms are named the norm of Abelian non-cyclic subgroups and the norm of cyclic subgroups of non-prime orders. Finite р-groups (р is prime, p not 2), finite 2-groups with non-cyclic center, periodic locally nilpotent groups, non-periodic groups with the free Abelian subgroup of rank 2, non-periodic locally soluble groups without the free Abelian subgroup of rank 2 with non-Dedekind norm of Abelian non-cyclic subgroups; non-periodic groups with non-Dedekind norm of subgroups of non-prime orders are described in Thesis. Connections between different generalized -norms: between the norm of Abelian non-cyclic subgroups, the norm non-cyclic subgroups, the norm of cyclic subgroups of non-prime orders, the norm of infinite cyclic subgroups are studed.