Residual properties of groups defined by basic commutators

Residual properties of groups defined by basic commutators

In this paper we study the residual nilpotence of groups defined by basic commutators. We prove that the so-called Hydra groups as well as certain of their generalizations and quotients are, in the main, residually torsion-free nilpotent. By way of contrast we give an example of a group defined by t...

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Bibliographic Details
Main Authors: Baumslag, Gilbert, Mikhailov, Roman
Format: Journal Article
Language:English
Published: 20-01-2013
Subjects:
Mathematics - Group Theory
Online Access:Get full text
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Summary:In this paper we study the residual nilpotence of groups defined by basic commutators. We prove that the so-called Hydra groups as well as certain of their generalizations and quotients are, in the main, residually torsion-free nilpotent. By way of contrast we give an example of a group defined by two basic commutators which is not residually torsion-free nilpotent.
DOI:10.48550/arxiv.1301.4629