Large groups of deficiency 1 |
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Authors: | J O Button |
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Institution: | (1) Selwyn College, University of Cambridge, Cambridge, CB3 9DQ, UK |
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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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Keywords: | |
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