Presentations of finite simple groups: profinite and cohomological approaches
نویسندگان
چکیده
منابع مشابه
Presentations of finite simple groups: profinite and cohomological approaches
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 H.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 H.G;M/ .18:5/ dim M . Mathematics Subject Classi...
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There is a constant C0 such that all nonabelian finite simple groups of rank n over Fq , with the possible exception of the Ree groups G2(3), have presentations with at most C0 generators and relations and total length at most C0(logn + log q). As a corollary, we deduce a conjecture of Holt: there is a constant C such that dimH2(G, M) ≤ C dimM for every finite simple group G, every prime p and ...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2007
ISSN: 1661-7207
DOI: 10.4171/ggd/22