We investigate asphericity of the relative group presentation ã€ˆG, t | atbtctdtet = 1ã€‰ and prove it aspherical provided the subgroup of G generated by {abâˆ’1, bcâˆ’1, cdâˆ’1, deâˆ’1} is neither finite cyclicâ€¦ (More)

A combinatorial group-theoretic hypothesis is presented that serves as a necessary and suucient condition for a union of connected Cock-croft two-complexes to be Cockcroft. This hypothesis has aâ€¦ (More)

We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. More generally, we prove that if n is a positive integer and Q is a finitely generated abelianâ€¦ (More)

We study a class of two-generator two-relator groups, denoted Jn(m, k), that arise in the study of relative asphericity as groups satisfying a transitional curvature condition. Particular instancesâ€¦ (More)

A group defined by a finite presentation with cyclic symmetry admits a shift automorphism that is periodic and word-length preserving. It is shown that if the presentation is combinatoriallyâ€¦ (More)

The Peiffer product of groups first arose in work of J.H.C. Whitehead on the structure of relative homotopy groups, and is closely related to problems of asphericity for two-complexes. We developâ€¦ (More)

We show that any finitely generated metabelian group can be embedded in a metabelian group of type F3. The proof builds upon work of G. Baumslag [4], who independently with V. R. Remeslennikov [10]â€¦ (More)

In this paper, we develop the low dimensional homotopy theory required for weighted combinatorial group theory. In [S97], the usual concepts of generators and relators of group presentations areâ€¦ (More)

We study a classM of cyclically presented groups that includes both finite and infinite groups and is defined by a certain combinatorial condition on the defining relations. This class includes manyâ€¦ (More)