This article is cited in 10 papers

Abelian groups with nilpotent commutators of endomorphisms

A. R. Chekhlov

Chair of Algebra, Tomsk State University, Tomsk, Russia

Abstract: We study classes of abelian groups with nilpotent commutators of their endomorphisms, as well as groups with a semirigid condition imposed on direct summands. We describe these groups amongst separable, vector, and algebraically compact torsion-free groups. We construct examples illustrating the distinction between considered classes of groups, as well as $E$-solvable and $E$-nilpotent groups.

Keywords: commutatorically invariant subgroup, $E$-nilpotent and $E$-solvable groups, $E$-engelian group, power $E$-commutant.

UDC: 512.541

Received: 09.09.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:10, 50–61

Bibliographic databases:

• 
•