My main interest, over the past 40 years, has been in computational group theory and semigroup theory. One of the main techniques that I have used is the Todd-Coxeter coset enumeration algorithm for which many computer implementations now exist. I have also been involved with the modified Todd-Coxeter coset enumeration algorithm and the Reidemeister-Schreier algorithm.

One particular application of the algorithms has been in the study of Fibonacci groups and various generalisations of such groups. I have also been interested in the occurrence of Fibonacci and Lucas numbers in the orders of certain finite groups. In addition, I have been interested in deficiency zero finite groups. Recent work has been concerned with presentations for finite simple groups and their covering groups and, in particular, I have been investigating whether such groups are efficient in terms of a technical definition of efficiency. I have also investigated symmetric presentations for groups. Another interest is investigating semigroup presentations. The efficiency of such semigroup presentations has been described.

See the the algebra group website for more information.

Joint Mathematical Council of the United Kingdom 2002 to 2012. Member of the United Kingdom Mathematics Trust (Member of Council 2008 - 2017).

Computational group theory; computational semigroup theory.