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.
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Gilbert Baumslag, Roman Mikhailov, Residual properties of groups defined by basic commutators. Groups Geom. Dyn. 8 (2014), no. 3, pp. 621–642DOI 10.4171/GGD/242