Presentations of Finite Simple Groups: a Quantitative Approach
نویسندگان
چکیده
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 every irreducible FpG-module M .
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ar X iv : m at h / 06 02 50 8 v 2 [ m at h . G R ] 1 9 N ov 2 00 7 PRESENTATIONS OF FINITE SIMPLE GROUPS : A QUANTITATIVE APPROACH
There is a constant C 0 such that all nonabelian finite simple groups of rank n over Fq, with the possible exception of the Ree groups 2 G 2 (3 2e+1), have presentations with at most C 0 generators and relations and total length at most C 0 (log n + log q). As a corollary, we deduce a conjecture of Holt: there is a constant C such that dim H 2 (G, M) ≤ C dim M for every finite simple group G, e...
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