Indicable Groups and Endomorphic Presentations

2011/12/08 by Mustafa Gokhan Benli, Benli, Mustafa Gokhan
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1112.1764

Will appear in Glasgow Mathematical Journal

arxiv created 2011/12/08 · arxiv updated 2011/12/09

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 \fieldZ where H has finite ascending endomorphic presentation.

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