# D. Holt, The word and conjugacy problems in hyperbolic groups

We review the definition and fundamental properties of (word) hyperbolic
groups. In particular, a finitely generated group is hyperbolic if and only
if it has a Dehn algorithm. This implies that the word problem can be
solved in linear time. A stronger result is that any word in the generators
of a hyperbolic group can be reduced to a normal form (the so-called shortlex
normal form) in linear time. We shall report on a recent result of
Holt and Epstein that the conjugacy problem in a hyperbolic group is
solvable in linear time. Finally, we discuss the relationships between
our methods and recent work Bridson and Howie on the conjugacy of finite
subsets in hyperbolic groups.

A.J. Duncan
Last modified: Wed Jun 2 17:51:05 BST 2004