This article is cited in 4 papers

The test rank of a soluble product of free Abelian groups

Ch. K. Gupta^a, E. I. Timoshenko<sup>b

a</sup> University of Manitoba
^b Novosibirsk State University of Architecture and Civil Engineering

Abstract: We consider the variety $\mathbb A^l$ of all soluble groups of derived length at most $l$, $l\geqslant2$. Suppose that a finitely generated group $G$ is a free product in the variety $\mathbb A^l$ of Abelian torsion-free groups. It is proved that the test rank of $G$ is one less than the number of factors. A test set of elements is written out explicitly.
Bibliography: 27 titles.

UDC: 512.54

MSC: Primary 20F16; Secondary 20E10, 20E36

Received: 14.03.2007

DOI: 10.4213/sm3852

 English version: Sbornik: Mathematics, 2008, 199:4, 495–510

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