ON PROJECTIVELY INERT SUBGROUPS OF COMPLETELY DECOMPOSABLE FINITE RANK GROUPS | Zendy

A. R. Chekhlov | Zendy; Olesya V. IVANETS | Zendy

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ON PROJECTIVELY INERT SUBGROUPS OF COMPLETELY DECOMPOSABLE FINITE RANK GROUPS

Author(s) -

A. R. Chekhlov,

Olesya V. IVANETS

Publication year - 2020

Publication title -

vestnik tomskogo gosudarstvennogo universiteta matematika i mekhanika

Language(s) - English

Resource type - Journals

eISSN - 2311-2255

pISSN - 1998-8621

DOI - 10.17223/19988621/67/6

Subject(s) - mathematics , rank (graph theory) , normal subgroup , combinatorics , invariant (physics) , index of a subgroup , prime (order theory) , characteristic subgroup , pure mathematics , group (periodic table) , chemistry , mathematical physics , organic chemistry

Let a group G be a finite direct sum of torsion-free rank 1 groups Gi. It is proved that every projectively inert subgroup of G is commensurate with a fully invariant subgroup if and only if all Gi are not divisible by any prime number p, and for different subgroups Gi and Gj their types are either equal or incomparable.

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