Results 1 to 10 of about 1,463 (124)
2-closures of primitive permutation groups of holomorph type
Open Mathematics, 2019 The 2-closure G(2) of a permutation group G on a finite set Ω is the largest subgroup of Sym(Ω) which has the same orbits as G in the induced action on Ω × Ω.
Jiangmin Pan
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Primitive permutation groups with a regular subgroup
Journal of Algebra, 2007 In the present paper all triples \((G,\Omega,X)\) are determined where \(G\) is a primitive permutation group acting on a finite set \(\Omega\) and containing a regular subgroup \(X\) in the case that the socle \(\text{soc}(G)\) of \(G\) is alternating, sporadic or an exceptional group of Lie type. Many further examples \((G,\Omega,X)\) are constructed
Barbara Baumeister
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Prime order derangements in primitive permutation groups [PDF]
Journal of Algebra, 2011 It is an easy exercise that any transitive permutation group \(G\) on a set \(\Omega\), \(|\Omega|\geq 2\), contains an element, which acts fixed point freely. These elements are called derangements. A much deeper result, using the classification of the finite simple groups, due to \textit{B. Fein}, \textit{W. M. Kantor} and \textit{M.
, , Timothy C Burness
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On the degress of primitive permutation groups
Mathematische Zeitschrift, 1982 Peter Cameron +2 more
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1-Designs Constructed from the Groups $PSL_{2}(81)$ and $PSL_{2}(89)$ [PDF]
Journal of Mahani Mathematical Research, 2022 In this paper, some designs from the primitive permutation representations of the groups $PSL_2(81)$ and $PSL_2(89)$ are constructed using the Key-Moori Method 1. We determine the automorphism groups of all the obtained designs and prove that the groups $
Reza Kahkeshani
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Primitive permutation IBIS groups [PDF]
Journal of Combinatorial Theory, Series A, 2021 Let $G$ be a finite permutation group on $Ω$. An ordered sequence of elements of $Ω$, $(ω_1,\dots, ω_t)$, is an irredundant base for $G$ if the pointwise stabilizer $G_{(ω_1,\dots, ω_t)}$ is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of $G$ have the same size we say that $G$ is an IBIS group.
Andrea Lucchini +2 more
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On the point stabilizer in a primitive permutation group
Mathematische Zeitschrift, 1973 Wolfgang Knapp, Knapp Wolfgang
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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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Sync-Maximal Permutation Groups Equal Primitive Permutation Groups [PDF]
, 2021 The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational problems related to synchronization and to the length of synchronizing words.
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