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Groups Geom. Dyn., 2014, Volume 8, Issue 3, Pages 621–642 (Mi ggd3)  

Residual properties of groups defined by basic commutators

G. Baumslaga, R. Mikhailovbc

a CUNY City Coll
b Steklov Math Inst, St Petersburg Dept, St Petersburg 191023, Russia
c St Petersburg State Univ, Chebyshev Lab, St Petersburg 199178, Russia

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.

Funding Agency Grant Number
CNS 111765
Ministry of Education and Science of the Russian Federation 11.G34.31.0026
MD-381.2014.1
Gazprom Neft
The research of the first author is supported by Grant CNS 111765. The research of the second author is supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government grant 11.G34.31.0026, and by JSC "Gazprom Neft", as well as by the RF Presidential grant MD-381.2014.1.


DOI: https://doi.org/10.4171/GGD/242


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