This article is cited 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.

UDC: 512.541

Received: 15.11.2012

DOI: 10.4213/mzm9378

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

Bibliographic databases:

• 
• 
• 
• 
• 
•