Intermediately fully invariant subgroups of abelian groups
- Authors: Chekhlov A.R.1
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Affiliations:
- Tomsk State University
- Issue: Vol 58, No 5 (2017)
- Pages: 907-914
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171512
- DOI: https://doi.org/10.1134/S0037446617050184
- ID: 171512
Cite item
Abstract
Describing intermediately fully invariant subgroups of divisible and torsion groups, we show that the intermediately fully invariant subgroups are direct summands in a completely decomposable group whose every homogeneous component is decomposable. For torsion groups, we find out when all their fully invariant subgroups are intermediately fully invariant; and for torsion-free groups, this question comes down to the reduced case. Also, in a torsion group that is the sum of cyclic subgroups, its subgroup is shown to be intermediately inert if and only if it is commensurable with some intermediately fully invariant subgroup.
About the authors
A. R. Chekhlov
Tomsk State University
Author for correspondence.
Email: cheklov@math.tsu.ru
Russian Federation, Tomsk