- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
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
© European Mathematical Society
4
2010
4
Largeness of LERF and 1-relator groups
Jack
Button
University of Cambridge, CAMBRIDGE, UNITED KINGDOM
1-relator groups, largeness, LERF
We consider largeness of groups given by a presentation of deficiency 1, where the group is respectively free-by-cyclic, LERF or 1-relator. We give the first examples of (finitely generated free)-by-ℤ word hyperbolic groups which are large, show that a LERF deficiency 1 group with first Betti number at least two is large or ℤ × ℤ and show that 2-generator 1relator groups where the relator has height 1 obey the dichotomy that either the group is large or all its finite images are metacyclic.
Group theory and generalizations
General
709
738
10.4171/GGD/102
http://www.ems-ph.org/doi/10.4171/GGD/102