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This article is cited in 6 scientific papers (total in 6 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.
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
Linking options:
https://www.mathnet.ru/eng/mzm9378https://doi.org/10.4213/mzm9378 https://www.mathnet.ru/eng/mzm/v94/i4/p620
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Abstract page: | 528 | Full-text PDF : | 157 | References: | 69 | First page: | 20 |
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