Groups, Geometry, and Dynamics

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Volume 4, Issue 4, 2010, pp. 835–846
DOI: 10.4171/GGD/109

Published online: 2010-10-15

On the extraction of roots in exponential A-groups

Stephen Majewicz[1] and Marcos Zyman[2]

(1) Kingsborough Community College, Brooklyn, USA
(2) Borough of Manhattan Community College, New York, USA

An exponential A-group is a group which comes equipped with an A-action (A is a commutative ring with unity), satisfying certain axioms. In this paper, we investigate some aspects of root extraction in the category of exponential A-groups. Of particular interest is the extraction of roots in nilpotent R-powered groups. Among other results, we prove that if R is a PID and G is a nilpotent R-powered group for which root extraction is always possible, then the torsion R-subgroup of G lies in the center. Furthermore, if the torsion R-subgroup is finitely R-generated, then G is torsion-free.

Keywords: Nilpotent R-powered group, exponential A-group, extraction of roots

Majewicz Stephen, Zyman Marcos: On the extraction of roots in exponential A-groups. Groups Geom. Dyn. 4 (2010), 835-846. doi: 10.4171/GGD/109