Torsion locally nilpotent groups with non-Dedekind norm of Abelian non-cyclic subgroups

Abstract

The authors study relations between the properties of torsion locally nilpotent groups and their norms of Abelian non-cyclic subgroups. The impact of the norm of Abelian non-cyclic subgroups on the properties of the group under the condition of norm non-Dedekindness is investigated. It was found that for these restrictions, torsion locally nilpotent groups are finite extensions of a quasi-cyclic subgroup and the structure of such groups is completely described.

Keywords

• torsion locally nilpotent group
• norm of a group
• non-dedekindness
• norm of abelian non-cyclic subgroups