- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:57
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
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1
2007
3
Reflections on the residual finiteness of one-relator groups
Gilbert
Baumslag
The City College of CUNY, NEW YORK, UNITED STATES
Charles
Miller III
University of Melbourne, MELBOURNE, Victoria, AUSTRALIA
Douglas
Troeger
The City College of CUNY, NEW YORK, UNITED STATES
One-relator group, residually finite, isomorphism problem
Let G = < a, b, … | r = 1 > be a one-relator group equipped with at least two generators. For all w which do not commute with r in the ambient free group on the generators a, b, …, the groups G(r,w) = < a,b, … | r r w = r 2 > are not residually finite and have the same finite images as G. The existence of this family of one-relator groups which are not residually finite reinforces what is becoming more obvious with time, that one-relator groups can be extremely complicated. This not only serves to underline the complexity of one-relator groups but provides us with the opportunity to raise a number of problems about these groups in the hope that they will stimulate further work on the conjugacy and isomorphism problems for one-relator groups as a whole.
Group theory and generalizations
General
209
219
10.4171/GGD/11
http://www.ems-ph.org/doi/10.4171/GGD/11