Recent work of Gromov, Epstein, Cannon, Thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups. (See [16],[17] andâ€¦ (More)

We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on aâ€¦ (More)

Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups haveâ€¦ (More)

We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating setâ€¦ (More)

We construct finite complete rewriting systems for two large classes of Artin groups: those of finite type, and those whose defining graphs are based on trees. The constructions in the two cases areâ€¦ (More)

A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of normal forms for the group. In this paper it is shown thatâ€¦ (More)

Let I denote the commutator ideal in the free associative algebra on m variables over an arbitrary field. In this article we prove there are exactly m! finite GrÃ¶bner bases for I , and uncountablyâ€¦ (More)

A finite complete rewriting system for a group is a finite presentation which gives an algorithmic solution to the word problem. Finite complete rewriting systems have proven to be useful objects inâ€¦ (More)

In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions C(1/6) and C(1/4) âˆ’ T (4) has the property that the set of allâ€¦ (More)