TY - JOUR
T1 - Presentations of finite simple groups
T2 - A computational approach
AU - Guralnick, R. M.
AU - Kantor, W. M.
AU - Kassabov, M.
AU - Lubotzky, A.
PY - 2011
Y1 - 2011
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=78751477689&partnerID=8YFLogxK
U2 - 10.4171/JEMS/257
DO - 10.4171/JEMS/257
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AN - SCOPUS:78751477689
SN - 1435-9855
VL - 13
SP - 391
EP - 458
JO - Journal of the European Mathematical Society
JF - Journal of the European Mathematical Society
IS - 2
ER -