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arXiv · 1112.1764

Indicable Groups and Endomorphic Presentations

Mustafa Gokhan Benli
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Abstract

In this note we look at presentations of subgroups of finitely presented groups with infinite cyclic quotients. We prove that if $H$ is a finitely generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic, then $H$ has ascending finite endomorphic presentation. It follows that any finitely presented indicable group without free semigroups has the structure of a semidirect product $H \rtimes \field{Z}$ where $H$ has finite ascending endomorphic presentation.

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Mustafa Gokhan Benli. 2011-12-08. Indicable Groups and Endomorphic Presentations. https://arxiv.org/abs/1112.1764

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