Presentations of Finite Simple Groups: a Computational Approach

@inproceedings{Kantor2009PresentationsOF,
  title={Presentations of Finite Simple Groups: a Computational Approach},
  author={William M. Kantor and Martin Kassabov},
  year={2009}
}
All nonabelian finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups G2(q), have presentations with at most 49 relations and bit-length O(log n+log q). Moreover, An and Sn have presentations with 3 generators, 7 relations and bit-length O(log n), while SL(n, q) has a presentation with 6 generators, 25 relations and bit-length O(log n + log q).