Results 11 to 20 of about 5,571,269 (248)
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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Factorizations of Primitive Permutation Groups [PDF]
Journal of Algebra, 1997 The author gives a complete classification of those finite primitive permutation groups which admit a factorization as a product of a point stabilizer and an automorphic image of it: \(G=G_\omega G^\alpha_\omega\). Using the types given in the O'Nan-Scott theorem the following cases are obtained: (i) If \(G\) is affine then \(G=(E_{2^3}L_3(2))\text{ wr
Barbara Baumeister, Baumeister, Barbara
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Pre-primitive permutation groups [PDF]
Journal of Algebra, 2023 A transitive permutation group $G$ on a finite set $Ω$ is said to be pre-primitive if every $G$-invariant partition of $Ω$ is the orbit partition of a subgroup of $G$. It follows that pre-primitivity and quasiprimitivity are logically independent (there are groups satisfying one but not the other) and their conjunction is equivalent to primitivity ...
Marina Anagnostopoulou-Merkouri +2 more
core +6 more sources
PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE [PDF]
Bulletin of the Australian Mathematical Society, 2013 AbstractThe primitive finite permutation groups containing a cycle are classified. Of these, only the alternating and symmetric groups contain a cycle fixing at least three points. This removes a primality condition from a classical theorem of Jordan. Some applications to monodromy groups are given, and the contributions of Jordan and Marggraff to this
Jones, G. A.
core +4 more sources
A classification of primitive permutation groups with finite stabilizers
Journal of Algebra, 2015 We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.
Simon Smith (17167579)
core +9 more sources
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
doaj +1 more source
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 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
openaire +5 more sources
On base sizes for symmetric groups [PDF]
, 2011 A base of a permutation group G on a set is a subset B of such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base.
Guralnick, Robert M. +7 more
core +2 more sources