Presentations of Finite Simple Groups: Profinite and Cohomological Approaches
Group Theory
2007-11-20 v1 Representation Theory
Abstract
We prove the following three closely related results. The first is that every finite simple group has a profinite presentation with 2 generators and at most 18 relations. The second is that if G is a finite simple group, F a field and M an FG-module, then the dimension of the second cohomology group of G with coefficients in M is at most 17.5 times the dimension of M. The third result is that we may replace 17.5 by 18.5 as long as M is faithful irreducible G-module. These last two results answer conjectures of Holt.
Keywords
Cite
@article{arxiv.0711.2817,
title = {Presentations of Finite Simple Groups: Profinite and Cohomological Approaches},
author = {Robert Guralnick and William M. Kantor and Martin Kassabov and Alex Lubotzky},
journal= {arXiv preprint arXiv:0711.2817},
year = {2007}
}
Comments
44 pages, to appear in Groups, Geometry and Dynamics