منابع مشابه
Orbit Coherence in Permutation Groups
For G ≤ Sym(Ω), let π(G) be the set of partitions of Ω given by the cycles of elements of G. Under the refinement order, π(G) admits join and meet operations. We say thatG is joinor meet-coherent if π(G) is joinor meet-closed, respectively. The centralizer in Sym(Ω) of any permutation g is shown to be meetcoherent, and join-coherent subject to a finiteness condition. Hence if G is a centralizer...
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This paper introduces the concept of orbit-homogeneity of permutation groups: a group G is orbitt-homogeneous if two sets of cardinality t lie in the same orbit of G whenever their intersections with each G-orbit have the same cardinality. For transitive groups, this coincides with the usual notion of t-homogeneity. This concept is also compatible with the idea of partition transitivity introdu...
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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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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 Group Theory
سال: 2014
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt-2013-0029