Journal article

ON THE FINITE PRESENTATION OF SUBDIRECT PRODUCTS AND THE NATURE OF RESIDUALLY FREE GROUPS

Martin R Bridson, James Howie, Charles F Miller, Hamish Short

AMERICAN JOURNAL OF MATHEMATICS | JOHNS HOPKINS UNIV PRESS | Published : 2013

Abstract

We establish virtual surjection to pairs (VSP) as a general criterion for the finite presentability of subdirect products of groups: if Γ1,.,Γn are finitely presented andS<Γ1×· · ·×Γn projects to a subgroup of finite index in each Γi×Γj, then S is finitely presentable, indeed there is an algorithm that will construct a finite presentation for S. We use the VSP criterion to characterize the finitely presented residually free groups. We prove that the class of such groups is recursively enumerable. We describe an algorithm that, given a finite presentation of a residually free group, constructs a canonical embedding into a direct product of finitely many limit groups. We solve the (multiple) c..

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University of Melbourne Researchers

Grants

Awarded by l'Alliance Scientific grant


Awarded by Leverhulme Trust


Awarded by Engineering and Physical Sciences Research Council


Funding Acknowledgements

This work grew out of a project funded by l'Alliance Scientific grant # PN 05.004. Research of the first author supported in part by an EPSRC Senior Fellowship and a Royal Society Nuffield Research Merit Award; research of the second author supported in part by Leverhulme Trust grant F/00 276/J.