Subgroup separability in tree groups and other graph groups
by
Tim Hsu
Pomona College
Coauthors: Daniel T. Wise (Brandeis University)

A graph group, or right-angled Artin group, is a group given by a presentation where the only relators are commutators of the generators. A graph group may be represented by a graph, with each generator represented by a vertex, and each commutator relator represented by an edge. For example, the graph group F₃×Z=<a, b, c, d | [a, b], [a, c], [a, d]> corresponds to a letter ``Y'' graph.

Recall that a subgroup H of a group G is said to be separable if H is the intersection of finite index subgroups of G. We show that if G is a graph group whose associated graph is a tree, then any quasiconvex subgroup of G is separable. We also discuss possibilities for, and obstructions to, extending this result to larger classes of graph groups.

Preprints available here

Date received: October 2, 2000