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My main interest, over the past 30 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 investigatingsemigroup presentations. The efficiency of such semigroup presentations has been described.
See the the algebra group website for more infomation.
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