Largeness of LERF and 1-relator groups

2008/03/26 by Button, Jack · 1 citation
#20F05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0803.3805

Abstract

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-(infinite cyclic) word hyperbolic groups which are large, show that a LERF deficiency 1 group with first Betti number at least 2 is large or the integers times the integers, and show that 2-generator 1-relator groups where the relator has height 1 obey the dichotomy that either the group is large or all its finite images are metacyclic.

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• Rank 1 phenomena for 1-relator and deficiency 1 groups

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