Geodesic
Largeness of LERF and 1-relator groups
Jack Oliver Button1
1University of Cambridge, UK
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 709-738

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DOI

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.
DOI : 10.4171/ggd/102
Classification : 20-XX, 00-XX
Mots-clés : 1-relator groups, largeness, LERF

Jack Oliver Button  1

1 University of Cambridge, UK 
Jack Oliver Button. Largeness of LERF and 1-relator groups. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 709-738. doi: 10.4171/ggd/102
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     year = {2010},
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     number = {4},
     doi = {10.4171/ggd/102},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/102/}
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