Presentations of finite simple groups: profinite and cohomological approaches
Robert M. Guralnick
University of Southern California, Los Angeles, United StatesWilliam M. Kantor
University of Oregon, Eugene, United StatesMartin Kassabov
Cornell University, Ithaca, United StatesAlexander Lubotzky
Hebrew University, Jerusalem, Israel

Abstract
We prove the following three closely related results:
- Every finite simple group G has a profinite presentation with 2 generators and at most 18 relations.
- 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.
- 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.
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