Presentations of finite simple groups: A computational approach

Abstract

All finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups 2G2(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 bitlength O(log n), while SL(n; q) has a presentation with 6 generators, 25 relations and bit-length O(log n + log q). © 2011 European Mathematical Society.