Fully inert subgroups of completely decomposable groups, having homogeneous components of the final rank

A. R. Chekhlov

Tomsk State University, 36 Lenin Ave., Tomsk, 634050 Russia

Abstract: For a considered class of completely decomposable torsion-free groups, comprising of itself all completely decomposable groups with final number homogeneous components, are found necessary and sufficient conditions, connected with types of component of the final rank, under which any fully inert subgroup commensurable with fully invariant. It is described of splitting mixed groups, in which any subgroup is projectively inert. It is shown that every projectively inert subgroups of the group form the sublattice in lattice of all its projectively inert subgroups.

Keywords: commensurable, fully inert subgroup, projectively inert subgroup, uniformly projectively inert subgroup.

UDC: 512.541

Received: 31.01.2022
Revised: 24.06.2022
Accepted: 29.06.2022

DOI: 10.26907/0021-3446-2022-12-91-100

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2022, 66:12, 82–90