This article is cited in 4 papers

Generating Elements for Groups of the Form $F/R'$

Ch. K. Gupta^a, E. I. Timoshenko

^a University of Manitoba

Abstract: Necessary and sufficient conditions are specified for a group of a specified type to be generated by its given elements ($F$ is a free product). Using these conditions (and relying essentially on the Shmel'kin embedding), we establish the criterion of being primitive for metabelian products of Abelian groups. A result by Birman and the primitivity criterion for free metabelian groups are generalized.

Keywords: metabelian products of Abelian groups, free metabelian group, generator.

UDC: 512.5

Received: 18.11.1999

 English version: Algebra and Logic, 2001, 40:3, 137–143

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