Results 11 to 20 of about 1,562 (223)
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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Normalizers of primitive permutation groups
Advances in Mathematics, 2017 44 pages, grant numbers updated, referee's comments ...
Robert M. Guralnick +2 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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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
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Invariance groups of finite functions and orbit equivalence of permutation groups
Open Mathematics, 2015 Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question.
Horváth Eszter K. +3 more
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On the Minimal Degree of a Primitive Permutation Group
Journal of Algebra, 1998 A previous result of \textit{M. W. Liebeck} and \textit{J. Saxl} [Proc. Lond. Math. Soc., III. Ser. 63, No. 2, 266-314 (1991; Zbl 0696.20004)] concerning the minimal degree of a primitive permutation group is improved. The main result is the following. Let \(G\) be a primitive permutation group acting on a set \(\Omega\) of size \(n\).
Guralnick, Robert, Magaard, Kay
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Pre-primitive permutation groups
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
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Normalisers of primitive permutation groups in quasipolynomial time [PDF]
Bulletin of the London Mathematical Society, 2020 11 ...
Roney-Dougal, Colva Mary, Siccha, Sergio
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Some Primitive Permutation Groups
Proceedings of the London Mathematical Society, 1985 Let \(\Omega\) be a countable infinite set. A subset \(\Sigma\) of \(\Omega\) is called a moiety iff \(\Sigma\) and \(\Omega\)-\(\Sigma\) are infinite. The following theorem is proved: If G is a primitive permutation group of \(\Omega\) that has no countable orbits on moieties, then G is 2-fold transitive. Furthermore, either G is highly transitive or \
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