Large Groups of Deficiency One

Details Large Groups of Deficiency One Large Groups of Deficiency One

2007-10-08

arxiv.org/abs/0710.1586v1

Mathematics

Group Theory

Covers similar ground to arXiv:math/0511715 but has been shortened and contains some new results in Sections 5,6,7

Scientific paper

We prove that if a group possesses a deficiency 1 presentation where one of the relators is a commutator then it is the integers times the integers, is 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 the integers times the integers as a 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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