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 2_G_2( 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 ).