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Fully Inert Subgroups of Completely Decomposable Groups with Homogeneous Components of Finite Rank

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Abstract

For the given class of completely decomposable torsion-free groups, which includes all completely decomposable groups with a finite number of homogeneous components, necessary and sufficient conditions are found associated with the types of homogeneous components of finite rank and such that any fully inert subgroup is commensurable with a fully invariant one. Splitting mixed groups with all their projectively inert subgroups are described. Uniformly projectively inert subgroups of the group are shown to form the sublattice in the lattice of all its projectively inert subgroups.

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ACKNOWLEDGMENTS

We thank a reviewer for a number of major remarks and recommendations, as well as for pointing out the class of groups N that extends the class supposed to be considered in Theorem 2.

Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2022-884).

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Authors and Affiliations

  1. Tomsk State University, 634050, Tomsk, Russia

    A. R. Chekhlov

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  1. A. R. Chekhlov
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Correspondence to A. R. Chekhlov.

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The author declares that he has no conflicts of interest.

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Translated by M. Talacheva

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Chekhlov, A.R. Fully Inert Subgroups of Completely Decomposable Groups with Homogeneous Components of Finite Rank. Russ Math. 66, 82–90 (2022). https://doi.org/10.3103/S1066369X22120015

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  • DOI: https://doi.org/10.3103/S1066369X22120015

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