Journal article

Structure and finiteness properties of subdirect products of groups

Martin R Bridson, Charles F Miller

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | LONDON MATH SOC | Published : 2009

Abstract

We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented subdirect product of free and surface groups virtually contains a term of the lower central series of the direct product or else fails to intersect one of the direct summands. This leads to a characterization of the finitely presented subgroups of the direct product of three free or surface groups and to a solution of the conjugacy problem for arbitrary finitely presented subgroups of direct products of surface groups.We obtain a formula for the first hom..

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University of Melbourne Researchers

Grants

Awarded by Swiss National Science Foundation and l'Alliance Scientific


Awarded by Engineering and Physical Sciences Research Council


Funding Acknowledgements

This research was supported by the Australian Research Council, the EPSRC of the United Kingdom, the Swiss National Science Foundation and l'Alliance Scientific (grant #PN 05.004). Author Martin R. Bridson was also supported in part by a Royal Society Nuffield Research Merit Award.