Dr Colin Campbell
Honorary Reader
 cmc@standrews.ac.uk
 Office
 122 MI
 Location
 Mathematical Institute
Research areas
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 ToddCoxeter coset enumeration algorithm for which many computer implementations now exist. I have also been involved with the modified ToddCoxeter coset enumeration algorithm and the ReidemeisterSchreier 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.
Selected publications

The Copson and Curle lectures
Campbell, C. M. & Robertson, E. F., 20 May 2020, Proceedings of the Conference on the History of Mathematics and Teaching of Mathematics, Miskolc, 2020. Kortesi, P. (ed.). Miskolc: University of Miskolc, 11 p.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Groups St Andrews 2017 in Birmingham
Campbell, C. M., Parker, C. W., Quick, M., Robertson, E. F. & RoneyDougal, C. M., Apr 2019, Cambridge University Press. 508 p. (London Mathematical Lecture Note Series 455)Research output: Book/Report › Book

Open access
Groups in Galway and Groups St Andrews conferences
Campbell, C. M., 23 May 2018, Proceedings of the Conference on History of Mathematics and Teaching of Mathematics, Miskolc, 2018. Miskolc: University of Miskolc, p. 2533Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

The recurrence sequences via polyhedral groups
Deveci, O., Akuzum, Y. & Campbell, C. M., 2018, In: Commun. Fac. Sci. Univ. Ank. Ser. A1. 67, 2, p. 99115Research output: Contribution to journal › Article › peerreview

A sufficient condition for coinciding the Green graphs of semigroups
Sorouhesh, M., Doostie, H. & Campbell, C. M., 2017, In: Journal of Mathematics and Computer Science. 17, 2, p. 216219 4 p.Research output: Contribution to journal › Article › peerreview

Open access
Notes on a semigroup related to the dicyclic group Q_{n}
Sorouhesh, M. R. & Campbell, C. M., 21 Sept 2017, In: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 25, 2, p. 149157 9 p.Research output: Contribution to journal › Article › peerreview

The FibonacciCirculant sequences and their applications
Deveci, Ö., Karaduman, E. & Campbell, C. M., 1 Dec 2017, In: Iranian Journal of Science and Technology, Transactions A: Science. 41, 4, p. 10331038 6 p.Research output: Contribution to journal › Article › peerreview

Groups St Andrews 2013
Campbell, C. M. (ed.), Quick, M. (ed.), Robertson, E. F. (ed.) & RoneyDougal, C. M. (ed.), 2015, Cambridge: Cambridge University Press. 500 p. (London Mathematical Society lecture note series ; vol. 422)Research output: Book/Report › Book

All simple groups with order from 1 million to 5 million are efficient
Robertson, E. F., Campbell, C. M., Havas, G. & Ramsay, C., Mar 2014, In: International Journal of Group Theory. 3, 1, p. 17–30 14 p.Research output: Contribution to journal › Article › peerreview

Noncommutative finite monoids of a given order n >= 4
Ahmadi, B., Campbell, C. M. & Doostie, H., 2014, In: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 22, 2, p. 2935 7 p.Research output: Contribution to journal › Article › peerreview