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arXiv · 0711.2817

Presentations of Finite Simple Groups: Profinite and Cohomological Approaches

Robert Guralnick·William M. Kantor·Martin Kassabov·Alex Lubotzky
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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.

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Robert Guralnick, William M. Kantor, Martin Kassabov, Alex Lubotzky. 2007-11-18. Presentations of Finite Simple Groups: Profinite and Cohomological Approaches. https://arxiv.org/abs/0711.2817

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