Symmetric representation of the elements of the Janko group \(J_ 1\) (Q674767)

In this paper with Hasan, Curtis continues his study of symmetric presentations of interesting groups, and develops some of the ideas further. Their main purpose is to demonstrate how Curtis' presentation of \(J_1\) can be enhanced to become a complete rewriting process, thereby enabling calculations in the group to take place with a much more compact representation of elements than permutations on 266 points would allow. There is some hope that these ideas might eventually permit computations in groups where the generating permutations themselves are too big to handle.