T-sets and permutation groups
نویسندگان
چکیده
منابع مشابه
Expanding Generator Sets for Solvable Permutation Groups
Let G = 〈S〉 be a solvable permutation group given as input by the generating set S. I.e. G is a solvable subgroup of the symmetric group Sn. We give a deterministic polynomial-time algorithm that computes an expanding generating set of size Õ(n2) for G. More precisely, given a λ < 1, we can compute a subset T ⊂ G of size Õ(n2) ( 1 λ )O(1) such that the undirected Cayley graph Cay(G,T ) is a λ-s...
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Let G = 〈S〉 be a solvable permutation group of the symmetric group Sn given as input by the generating set S. We give a deterministic polynomial-time algorithm that computes an expanding generating set of size Õ(n) for G. More precisely, the algorithm computes a subset T ⊂ G of size Õ(n)(1/λ) such that the undirected Cayley graph Cay(G, T ) is a λ-spectral expander (the Õ notation suppresses lo...
متن کاملNear-Optimal Expanding Generator Sets for Solvable Permutation Groups
Let G = 〈S〉 be a solvable subgroup of the symmetric group Sn given as input by the generator set S. We give a deterministic polynomialtime algorithm that computes an expanding generator set of size Õ(n) for G. As a byproduct of our proof, we obtain a new explicit construction of ε-bias spaces of size Õ(npoly(log d))( 1 ε ) for the groups Zd .
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From any given permutation group acting on a finite collection of n points one can form, for each positive integer k<=n, two permutation groups by considering respectively the permutations induced by the given group on the unordered sets of k distinct points and those induced on the ordered sets of k distinct points. We consider relations between these two groups. Our main object is to prove Th...
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By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1974
ISSN: 0021-8693
DOI: 10.1016/0021-8693(74)90212-9