Groups, Geometry, and Dynamics


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Volume 8, Issue 3, 2014, pp. 621–642
DOI: 10.4171/GGD/242

Published online: 2014-10-02

Residual properties of groups defined by basic commutators

Gilbert Baumslag and Roman Mikhailov[1]

(1) Steklov Mathematical Institute, Moscow, Russian Federation

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.

Keywords: Commutator calculus, residual nilpotence, basic commutators, one-relator groups

Baumslag Gilbert, Mikhailov Roman: Residual properties of groups defined by basic commutators. Groups Geom. Dyn. 8 (2014), 621-642. doi: 10.4171/GGD/242