Presentations of Finite Simple Groups: Profinite and Cohomological Approaches

Details Presentations of Finite Simple Groups: Profinite and Cohomological Approaches Presentations of Finite Simple Groups: Profinite and Cohomological Approaches

2007-11-18

arxiv.org/abs/0711.2817v1

Mathematics

Group Theory

44 pages, to appear in Groups, Geometry and Dynamics

Scientific paper

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.

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