منابع مشابه
Presentations of Finite Simple Groups: a Quantitative Approach
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 ...
متن کاملPresentations 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...
متن کاملPresentations of Finite Simple Groups: a Computational Approach
All nonabelian finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups G2(q), have presentations with at most 49 relations and bit-length O(log n+log q). Moreover, An and Sn have presentations with 3 generators, 7 relations and bit-length O(log n), while SL(n, q) has a presentation with 6 generators, 25 relations and bit-length O(log n + ...
متن کاملFinite Presentations of Hyperbolic Groups
Although (G, dS) is not a geodesic metric space, its Cayley graph ΓS(G) is, and it is the geodesics that provide the natural relationship between dS and the Cayley graph. Let G be the vertex set on the Cayley graph. Two vertices g and h are adjacent in ΓS(G) precisely when g −1h ∈ S or h−1g ∈ S, in which case dS(g, h) = 1. Inductively, it follows that dS(g, h) = n precisely when the shortest pa...
متن کاملShort Presentations for Finite Groups
We conjecture that every nite group G has a short presentation (in terms of generators and relations) in the sense that the total length of the relations is (log jGj) O(1). We show that it suuces to prove this conjecture for simple groups. Motivated by applications in computational complexity theory, we conjecture that for nite simple groups, such a short presentation is computable in polynomia...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1988
ISSN: 0263-6115
DOI: 10.1017/s1446788700030068