JournalsjemsVol. 13, No. 2pp. 391–458

Presentations of finite simple groups: a computational approach

  • Alexander Lubotzky

    Hebrew University, Jerusalem, Israel
  • Robert M. Guralnick

    University of Southern California, Los Angeles, United States
  • William M. Kantor

    University of Oregon, Eugene, United States
  • Martin Kassabov

    Cornell University, Ithaca, United States
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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).

Cite this article

Alexander Lubotzky, Robert M. Guralnick, William M. Kantor, Martin Kassabov, Presentations of finite simple groups: a computational approach. J. Eur. Math. Soc. 13 (2011), no. 2, pp. 391–458

DOI 10.4171/JEMS/257