Permutation groups on unordered sets I
نویسندگان
چکیده
منابع مشابه
Transitivity of finite permutation groups on unordered sets
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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Siemons, J., Permutation groups on unordered sets II; On a theorem of Frucht, Discrete Mathematics 118 (1993) 275-278. We show that every group is the full automorphism group of an unordered k-relation for given k 2 2 on some suitable set. We are also concerned with the cardinality of a minimal representation with this property as a function of k. A permutation group (G, 52) on a finite or infi...
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For a set Ω an unordered relation on Ω is a family R of subsets of Ω . If R is such a relation we let G(R) be the group of all permutations on Ω that preserve R, that is g belongs to G(R) if and only if x ∈R implies x ∈R. We are interested in permutation groups which can be represented as G= G(R) for a suitable unordered relation R on Ω . When this is the case, we say that G is defined by the r...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 1984
ISSN: 0003-889X,1420-8938
DOI: 10.1007/bf01190948