Results 21 to 30 of about 5,571,269 (248)
Topics in computational group theory : primitive permutation groups and matrix group normalisers [PDF]
, 2012 Part I of this thesis presents methods for finding the primitive permutation groups of degree d, where 2500 ≤ d < 4096, using the O'Nan-Scott Theorem and Aschbacher's theorem. Tables of the groups G are given for each O'Nan-Scott class.
Coutts, Hannah Jane
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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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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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Most primitive groups are full automorphism groups of edge-transitive hypergraphs [PDF]
, 2014 We prove that, for a primitive permutation group G acting on a set X of size n, other than the alternating group, the probability that Aut (X,YG) = G for a random subset Y of X, tends to 1 as n → ∞.
Cameron, Peter Jephson +2 more
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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.
Yu Xue, Pan Jiangmin
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Minimal and random generation of permutation and matrix groups [PDF]
, 2012 We prove explicit bounds on the numbers of elements needed to generate various types of finite permutation groups and finite completely reducible matrix groups, and present examples to show that they are sharp in all cases.
Derek F. Holt +5 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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Most switching classes with primitive automorphism groups contain graphs with trivial groups [PDF]
, 2015 The operation of switching a graph Gamma with respect to a subset X of the vertex set interchanges edges and non-edges between X and its complement, leaving the rest of the graph unchanged.
Cameron, Peter Jephson, Spiga, Pablo
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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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