On strongly invariant subgroups of Abelian groups

Chekhlov, A. R.

doi:10.1134/s0001434617070112

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Lemma 223 (1) If G Is a Torsion-free Group And1

Introduction and Definitions1

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2018

2023

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Cited by 5 publications

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“…Note that some other interesting results for si-subgroups and irreducible groups are proved in [2,3], respectively. We now will give some additions to that as follows.…”

Section: Lemma 223 (1) If G Is a Torsion-free Group Andmentioning

confidence: 96%

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On Abelian Groups Having All Proper Fully Invariant Subgroups Isomorphic

Chekhlov

Danchev

2015

Communications in Algebra

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We introduce two classes of abelian groups which have either only trivial fully invariant subgroups or all their nontrivial (respectively nonzero) fully invariant subgroups are isomorphic, called IFI-groups and strongly IFI-groups, such that every strongly IFIgroup is an IFI-group, respectively. Moreover, these classes coincide when the groups are torsion-free, but are different when the groups are torsion as well as, surprisingly, mixed groups cannot be IFI-groups. We also study their important properties as our results somewhat contrast with those from [13] and [14].

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“…Note that some other interesting results for si-subgroups and irreducible groups are proved in [2,3], respectively. We now will give some additions to that as follows.…”

Section: Lemma 223 (1) If G Is a Torsion-free Group Andmentioning

confidence: 96%

“…Let us notice that the si-subgroups were intensively studied in [1,3], respectively, as well as in some other relevant articles cited therewith.…”

Section: Introduction and Definitionsmentioning

confidence: 99%