a1 Department of Mathematics, University of Newcastle, Newcastle, NSW 2308, Australia, e-mail: email@example.com
Some structure theorems for totally disconnected groups are described. These theorems produce a certain positive integer valued function, called the scale function, on each totally disconnected group. The scale function has properties connected to the structure of the group and can be used to prove some conjectures of Hofmann and Mukherjea.
(Received August 04 1994)