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Large groups of deficiency 1

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Abstract

We prove that if a group possesses a deficiency 1 presentation where one of the relators is a commutator, then it is ℤ × ℤ, large or is as far as possible from being residually finite. Then we use this to show that a mapping torus of an endomorphism of a finitely generated free group is large if it contains a ℤ × ℤ subgroup of infinite index, as well as showing that such a group is large if it contains a Baumslag-Solitar group of infinite index and has a finite index subgroup with first Betti number at least 2. We give applications to free by cyclic groups, 1 relator groups and residually finite groups.

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  1. Selwyn College, University of Cambridge, Cambridge, CB3 9DQ, UK

    J. O. Button

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Button, J.O. Large groups of deficiency 1. Isr. J. Math. 167, 111–140 (2008). https://doi.org/10.1007/s11856-008-1043-9

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  • DOI: https://doi.org/10.1007/s11856-008-1043-9

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