Permutation Groups

I first learnt the basic theory of permutation groups as a doctoral student but it wasn't until I wanted to use them for computer calculation that I became fascinated by them. My early work [1,2,3,4,5,6,7] was largely on doubly transitive groups and their tendency to be groups of automorphisms of block designs. Later on, at irregular intervals [8,9,10,11], I returned to the more computational aspects of their study.

In those early days permutation group theory was a possible plank in the international project to classify finite simple groups. Sadly, once this was achieved, the impetus rather disappeared although even now there is some interest in computer algorithms for explicit calculation.

Papers on permutation groups

  1. Two theorems on doubly transitive permutation groups, J. London Math. Soc. (2), 6 (1973), 269-274.
  2. Doubly transitive but not doubly primitive permutation groups, J. London Math. Soc. (2), 7 (1974), 632-634.
  3. Doubly transitive but not doubly primitive permutation groups II, J. London Math. Soc. (2), 10 (1975), 53-60.
  4. An algorithm for computing the blocks of a permutation group, Math. Comp. 29 (1975), 911-913.
  5. On rank 3 groups having \lambda=0, Can. J. Math. 29 (1977), 845-847.
  6. On the normal structure of a one-point stabiliser in a doubly transitive permutation group, J. Austral. Math. Soc. 25 (1978), 145-166 (with C.E. Praeger).
  7. Some permutation groups of degree p=6q+1, Archiv d. Math. 32 (1979), 530-532.
  8. Permutation groups and set union algorithms, Computer J. 23, 2 (1980), 187.
  9. Group theory on a micro-computer, in Proceedings of the International Conference on Computational Group Theory (Durham, August 1982), 275-280 (Academic Press, London 1984) (with R.A. Hassan and M.P. Thorne).
  10. Computing Sylow subgroups of permutation groups, Twenty-first Southeastern Conference on Combinatorics, Graph Theory and Computing, (Boca Raton, February 1990), Congressus Numerantium 79 (1990), 55-60 (with P.M. Neumann).
  11. A new algorithm for testing the regularity of a permutation group, Twenty-third Southeastern Conference on Combinatorics, Graph Theory and Computing, (Boca Raton, February 1992), Congressus Numerantium 90 (1992), 151-160 (with V. Acciaro).