JournalsggdVol. 1 , No. 4DOI 10.4171/ggd/22

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
Presentations of finite simple groups: profinite and cohomological approaches cover

Abstract

We prove the following three closely related results:

  1. Every finite simple group G has a profinite presentation with 2 generators and at most 18 relations.
  2. If G is a finite simple group, F a field and M is an FG-module, then  dim H2(G,M) ≤ (17.5) dim M.
  3. If G is a finite group, F a field and M is an irreducible faithful FG-module, then dim H2(G,M) ≤ (18.5) dim M.