Residual properties of groups defined by basic commutators

2013/01/20 by Gilbert Baumslag, Baumslag, Gilbert, Roman Mikhailov +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1301.4629

17 pages

arxiv created 2013/08/28 · arxiv updated 2013/08/29

Abstract

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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