Short Presentations for Finite Groups
نویسندگان
چکیده
منابع مشابه
Short 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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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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1997
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6980