7 citations · 12 across the 5 of their papers we have counts for
5 papers
Pairs of valuations and the geometry of soluble groups
Andrew D. Warshall
We introduce the concepts of a pair of valuations and a good generating set and show how they can be used to prove geometric properties of soluble groups.
Strongly t-logarithmic t-generating sets: Geometric properties of some soluble groups
Andrew D Warshall
We introduce the concept of a strongly t-logarithmic t-generating set for a Z[t,t^{-1}]-module, which enables us to prove that a large class of soluble groups are not almost convex…
A group with deep pockets for all finite generating sets
Andrew D. Warshall
We show that the discrete Heisenberg group has unbounded dead-end depth with respect to every finite generating set. We also show that, in contrast, it has bounded retreat depth.
Deep pockets in lattices and other groups
Andrew D. Warshall
We show the nonexistence of deep pockets in a large class of groups, extending a result of Bogopol'skii. We then give examples of important groups (such as Nil and Sol) which have…
Arbitrarily large finite quotients imply no uniform bound on depth
Andrew D. Warshall
We show that any group with arbitrarily large finite quotients admits generating sets with respect to which it has arbitrarily large finite dead-end depth. This extends a joint res…