Permutation groups, minimal degrees and quantum computing
نویسندگان
چکیده
منابع مشابه
Permutation groups, minimal degrees and quantum computing
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group H ≤ Sn of minimal degree m and on the number of its elements of any given support. These results contribute to the foundations of a non-commutative coding theory. A main application of our results concerns the Hidden Subgroup Problem...
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We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If K is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra K: this is a refinement of Wang’s universality theorem for the (compact) quantum permutation group. We also prove a structural result for Hopf algebras having a non-...
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for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2007
ISSN: 1661-7207
DOI: 10.4171/ggd/24