A subgroup of a product of n surface groups is of type FPn if and only if it contains a subgroup of finite index that is itself a product of (at most n) surface groups.

We give examples of direct products of three hyperbolic groups in which there cannot exist an algorithm to decide which finitely presented subgroups are isomorphic. In [1] Baumslag, Short and theâ€¦ (More)

We show that the finitely presented groups with unsolvable word problem given by the Boone-Britton construction have cohomological dimension 2. More precisely we show these groups can be obtainedâ€¦ (More)

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 HNNâ€¦ (More)

If Î“1, . . . ,Î“n are limit groups and S âŠ‚ Î“1 Ã— Â· Â· Â· Ã— Î“n is of type FPn(Q) then S contains a subgroup of finite index that is itself a direct product of at most n limit groups. This answers aâ€¦ (More)

We establish virtual surjection to pairs (VSP) as a general criterion for the finite presentability of subdirect products of groups: if Î“1, . . . ,Î“n are finitely presented and S < Î“1Ã—Â· Â· Â·Ã—Î“nâ€¦ (More)

Let G D ha; b; : : : j r D 1i be a one-relator group equipped with at least two generators. For all w which do not commute with r in the ambient free group on the generators a, b, ..., the groupsâ€¦ (More)

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups ofâ€¦ (More)

We give a criterion for fibre products to be finitely presented and use it as the basis of a construction that encodes the pathologies of finite group presentations into pairs of groups P âŠ‚ G where Gâ€¦ (More)

The arguments of Cannon, Floyd, Grayson and Thurston [CFGT] showing that solvegeometry groups are not almost convex apply to solvable Baumslag-Solitar groups.