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
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..View full abstract
Awarded by l'Alliance Scientific grant
Awarded by Leverhulme Trust
Awarded by Engineering and Physical Sciences Research Council
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.