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.
1
The City College of New York, United States
2
Steklov Mathematical Institute, Moscow, Russian Federation
Gilbert Baumslag; Roman Mikhailov. Residual properties of groups defined by basic commutators. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 621-642. doi: 10.4171/ggd/242
@article{10_4171_ggd_242,
author = {Gilbert Baumslag and Roman Mikhailov},
title = {Residual properties of groups defined by basic commutators},
journal = {Groups, geometry, and dynamics},
pages = {621--642},
year = {2014},
volume = {8},
number = {3},
doi = {10.4171/ggd/242},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/242/}
}
TY - JOUR
AU - Gilbert Baumslag
AU - Roman Mikhailov
TI - Residual properties of groups defined by basic commutators
JO - Groups, geometry, and dynamics
PY - 2014
SP - 621
EP - 642
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/242/
DO - 10.4171/ggd/242
ID - 10_4171_ggd_242
ER -
%0 Journal Article
%A Gilbert Baumslag
%A Roman Mikhailov
%T Residual properties of groups defined by basic commutators
%J Groups, geometry, and dynamics
%D 2014
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%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/242/
%R 10.4171/ggd/242
%F 10_4171_ggd_242
