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Mat. Zametki, 2013, Volume 94, Issue 4, Pages 620–627 (Mi mz9378)  

This article is cited in 4 scientific papers (total in 4 papers)

Torsion-Free Weakly Transitive $E$-Engel Abelian Groups

A. R. Chekhlov

Tomsk State University

Abstract: It is proved that if all the endomorphisms of a reduced torsion-free weakly transitive Abelian group are bounded right-nilpotent, then its ring of endomorphisms is commutative. The ring of endomorphisms of a torsion-free Abelian group with periodic group of automorphisms and Engel ring of endomorphisms is also commutative.

Keywords: $E$-Engel Abelian group, weakly transitive group, torsion-free Abelian group, ring of endomorphisms, periodic group of automorphisms, $n$-step Engel ring, Lie algebra, $E$-nilpotent group, nilpotent element of a ring.

DOI: https://doi.org/10.4213/mzm9378

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English version:
Mathematical Notes, 2013, 94:4, 583–589

Bibliographic databases:

UDC: 512.541
Received: 15.11.2012

Citation: A. R. Chekhlov, “Torsion-Free Weakly Transitive $E$-Engel Abelian Groups”, Mat. Zametki, 94:4 (2013), 620–627; Math. Notes, 94:4 (2013), 583–589

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chekhlov A.R., Danchev P.V., “on Commutator Fully Transitive Abelian Groups”, J. Group Theory, 18:4 (2015), 623–647  crossref  mathscinet  zmath  isi  elib
    2. Chekhlov A.R., Danchev P.V., “on Abelian Groups Having All Proper Fully Invariant Subgroups Isomorphic”, Commun. Algebr., 43:12 (2015), 5059–5073  crossref  mathscinet  zmath  isi  elib
    3. A. R. Chekhlov, “On Abelian groups with commutative commutators of endomorphisms”, J. Math. Sci., 230:3 (2018), 502–506  mathnet  crossref  mathscinet  elib
    4. V. M. Misyakov, “Vpolne tranzitivnye, tranzitivnye abelevy gruppy i nekotorye ikh obobscheniya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 4(42), 23–32  mathnet  crossref  elib
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