Groups, Geometry, and Dynamics
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Published online: 2014-10-02
Residual properties of groups defined by basic commutatorsGilbert Baumslag and Roman Mikhailov (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