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- Tim R. Riley, Andrew D. Warshall
- IJAC
- 2006

The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius dA(1, g) closed ball, in the word metric dA. We exhibit a finitely presented group K with two finite generating sets A and B such that dead-end depth is unbounded on K with respect to A but is bounded above by three with respect… (More)

We show the nonexistence of deep pockets in a large class of groups, extending a result of Bogopol’skĭi. We then give examples of important groups (namely lattices in Nil and Sol) which have deep pockets.

We show that the discrete Heisenberg group has unbounded deadend depth with respect to every finite generating set. We also show that, in contrast, it has bounded retreat depth.

- Harry P Warren, Jay Bookbinder, +4 authors Andrew D. Warshall
- 1999

The ability of the Transition Region and Coronal Explorer (TRACE) to image solar plasma over a wide range of temperatures ( –10 K) at high spatial resolution (00.5 pixels) makes it a unique instrument for observing 4 T ∼ 10 e solar flares. We present TRACE and Yohkoh observations of an M2.4 two-ribbon flare that began on 1999 July 25 at about 13:08 UT. We… (More)

The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius dA(1, g) closed ball, in the word metric dA. We exhibit a finitely presented group K with two finite generating sets A and B such that dead-end depth is unbounded on K with respect to A but is at most two with respect to B. 2000… (More)

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.

We introduce the concept of a strongly t-logarithmic t-generating set for a Z ˆ t, t ̃ -module, which enables us to prove that a large class of soluble groups are not almost convex. We also prove some results about dead-end depth.

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