Results 21 to 30 of about 55,118 (252)
Classifying primitive solvable permutation groups of rank 5 and 6 [PDF]
Journal of group theroy, 2023 Let 𝐺 be a finite solvable permutation group acting faithfully and primitively on a finite set Ω. Let G 0 G_{0} be the stabilizer of a point 𝛼 in Ω.
Anakin Dey +4 more
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Base sizes of primitive groups of diagonal type
Forum of Mathematics, Sigma, 2023 Let G be a permutation group on a finite set $\Omega $ . The base size of G is the minimal size of a subset of $\Omega $ with trivial pointwise stabiliser in G. In this paper, we extend earlier work of Fawcett by determining the precise base
Hong Yi Huang
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ON SOME VERTEX-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS
Ural Mathematical Journal, 2022 In the present paper, we classify abelian antipodal distance-regular graphs \(\Gamma\) of diameter 3 with the following property: \((*)\) \(\Gamma\) has a transitive group of automorphisms \(\widetilde{G}\) that induces a primitive almost simple ...
Ludmila Yu. Tsiovkina
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ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP [PDF]
Nagoya mathematical journal, 2020 Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ .
Nick Gill, Bianca Lod'a, Pablo Spiga
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On primitive 2-closed permutation groups of rank at most four [PDF]
J. Comb. Theory B, 2021 We characterise the primitive 2-closed groups $G$ of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or $G\leqslant \mathrm{A}\Gamma\mathrm{
Michael Giudici +2 more
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Imprimitive permutations in primitive groups
Journal of Algebra, 2017 The goal of this paper is to study primitive groups that are contained in the union of maximal (in the symmetric group) imprimitive groups. The study of types of permutations that appear inside primitive groups goes back to the origins of the theory of permutation groups. However, this is another instance of a situation common in mathematics in which a
J. Araújo +5 more
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Primitive permutation groups and strongly factorizable transformation semigroups [PDF]
Journal of Algebra, 2019 Let $\Omega$ be a finite set and $T(\Omega)$ be the full transformation monoid on $\Omega$. The rank of a transformation $t\in T(\Omega)$ is the natural number $|\Omega t|$.
J. Ara'ujo, W. Bentz, P. Cameron
semanticscholar +1 more source
Bounding the composition length of primitive permutation groups and completely reducible linear groups [PDF]
Journal of the London Mathematical Society, 2017 We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups.
S. Glasby +3 more
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On Transitive Permutation Groups with Primitive Subconstituents [PDF]
Bulletin of the London Mathematical Society, 1999 The authors investigate transitive permutation groups \(G\) acting on a set \(\Omega\) of arbitrary cardinality such that the stabilizer \(G_\omega\) in \(G\) of a point \(\omega\in\Omega\) acts primitively on each nontrivial orbit (i.e. of size at least \(2\)) in \(\Omega\).
Pasechnik, Dmitrii V. +1 more
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Primitive Permutation Groups with Primitive Jordan Sets
Journal of the London Mathematical Society, 1996 Let \(\Omega\) be a set and \(G\) a group of permutations of \(\Omega\). A subset \(\Sigma\) of \(\Omega\) is said to be a Jordan set (for \(G\) in \(\Omega\)) if \(|\Sigma|>1\) and there is a subgroup \(H\) of \(G\) that is transitive on \(\Sigma\) and fixes the complement \(\Omega\setminus\Sigma\) pointwise.
Adeleke, SA, Neumann, P
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