ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 20,54 Jewett, Rumara, State University of New York at Albany, Albany, NY, USA Almost Convexity of a Certain Nilpotent Group Let G be a group generated by (g_{i}), and let S(n) be the sphere of radius n in the Cayley graph of G constructed with (g_{i}). Choose any two elements g and g′ in S(n) two units apart. If a connecting path exists between them of length bounded by p, with p independent of n, we say that G is almost convex. The nilpotent group (x, y|[[x, [x, y]], x] = [[x, [x, y]], y] = [[x, y], y] = 1) can be shown to be almost convex using geometric methods. Referemce: R. Jewett and S. Plotnick Almost Convexity of Certain Nilpotent Groups (preprint)