Presentations of finite simple groups: profinite and cohomological approaches

  • 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
  • Alexander Lubotzky

    Hebrew University, Jerusalem, Israel

Abstract

We prove the following three closely related results:

  1. Every finite simple group has a profinite presentation with 2 generators and at most 18 relations.
  2. If is a finite simple group, a field and is an -module, then  .
  3. If is a finite group, a field and is an irreducible faithful -module, then .

Cite this article

Robert M. Guralnick, William M. Kantor, Martin Kassabov, Alexander Lubotzky, Presentations of finite simple groups: profinite and cohomological approaches. Groups Geom. Dyn. 1 (2007), no. 4, pp. 469–523

DOI 10.4171/GGD/22