Texas A&M University, Department of
Mathematics, 216 Milner Hall, 30th of April 2008, 3:00-3:50
Groups and Dynamics Seminar
The shortest language spoken by a group
Susan Hermiller of University of Nebraska
Let Geo(G,X) be the set of all words over a generating
set X of a group G that label geodesic paths in the corresponding
Cayley graph for G. For many classes of groups, including
word hyperbolic groups, Coxeter groups, and
and Garside groups, it is known that there are finite generating
sets X for which Geo(G,X) is regular.
In this talk I will discuss geometric and combinatorial
properties of finitely generated groups for which Geo(G,X)
satisfies stronger language-theoretic conditions, in particular
lying in the classes of star-free, locally excluding, and
locally testable languages.