This article is cited in 13 papers

Commutator invariant subgroups of abelian groups

A. R. Chekhlov

Tomsk State University, Tomsk, Russia

Abstract: We describe the commutator invariant subgroups of a nonreduced abelian group. We find out when all commutator invariant subgroups of a separable group and an algebraically compact torsion-free group are fully invariant and describe the $E$-centers and $E$-commutants of these and some other groups.

Keywords: endomorphism ring, fully invariant subgroup, commutator of an endomorphism, $E$-center, $E$-commutant.

UDC: 512.541

Received: 15.02.2010

 English version: Siberian Mathematical Journal, 2010, 51:5, 926–934

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