This article is cited in 5 papers

MATHEMATICS

E-engelian abelian groups of step $\le2$

A. R. Chekhlov

Tomsk State University

Abstract: It is proved that periodicity of the automorphism group or weak transitivity of an E-engelian torsion free group of step $\le2$ implies commutativity of its endomorphism ring. Some properties of the engelian ring of step $2$ are established. It is also shown that the endomorphism ring of a weakly transitive torsion free group is semiprime.

Keywords: commutator of endomorphisms, prime radical, nil radical, E-solvable group, weakly transitive torsion free group.

UDC: 512.541+512.552


Accepted: November 3, 2011