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

Authors

  • T.D. Lukashova Makarenko Sumy State Pedagogical University, Sumy, Ukraine
  • M.G. Drushlyak Makarenko Sumy State Pedagogical University, Sumy, Ukraine https://orcid.org/0000-0002-9648-2248
https://doi.org/10.15330/cmp.14.1.247-259

Keywords:

torsion locally nilpotent group, norm of a group, non-Dedekindness, norm of Abelian non-cyclic subgroups
Published online: 2022-06-30

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.

Article metrics
How to Cite
(1)
Lukashova, T.; Drushlyak, M. Torsion Locally Nilpotent Groups With Non-Dedekind Norm of Abelian Non-Cyclic Subgroups. Carpathian Math. Publ. 2022, 14, 247-259.