This article is cited in 13 papers

Totally Transitive Torsion-Free Groups of Finite $p$-Rank

A. R. Chekhlov


Abstract: Totally transitive torsion-free groups all non-zero endomorphisms of which are monomorphisms are studied. Such are characterized in terms of modules over some rings with specific properties. Also, a structural description is provided for quasihomogeneous, totally transitive, torsion-free groups $A$ of finite $p$-rank, for at least one prime $p$ not dividing $A$.

Keywords: totally transitive torsion-free group, quasihomogeneous totally transitive group, endomorphism, monomorphism.

UDC: 512.541

Received: 21.04.1999
Revised: 20.07.2001

 English version: Algebra and Logic, 2001, 40:6, 391–400

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