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Transitive Subgroups of Primitive Permutation Groups
Journal of Algebra, 2000 The authors classify the primitive permutation groups \(G\) which possess a transitive subgroup which does not contain a nontrivial subnormal subgroup of \(G\). The conclusion is that such primitive groups are rather rare, and that their existence is intimately connected with factorisations of almost simple groups.
Liebeck, Martin W. +2 more
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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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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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Base sizes for simple groups and a conjecture of Cameron [PDF]
, 2009 Let G be a permutation group on a finite set ?. A base for G is a subset B C_ ? whose pointwise stabilizer in G is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ?
Burness, TC +5 more
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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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Permutation groups, simple groups and sieve methods [PDF]
, 2005 We show that the number of integers n ≤ x which occur as indices of subgroups of nonabelian finite simple groups, excluding that of An-1 in An, is ∼ hx/log x, for some given constant h.
Heath-Brown, D. R. +9 more
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Derangements in cosets of primitive permutation groups [PDF]
Journal of Group Theory, 2014 Abstract Motivated by questions arising in connection with branched coverings of connected smooth projective curves over finite fields, we study the proportion of fixed-point free elements (derangements) in cosets of normal subgroups of primitive permutations groups.
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On derangements in simple permutation groups
Forum of Mathematics, SigmaLet $G \leqslant \mathrm {Sym}(\Omega )$ be a finite transitive permutation group and recall that an element in G is a derangement if it has no fixed points on $\Omega $ . Let $\Delta (G)$ be the set of derangements in G and define
Timothy Burness, Marco Fusari
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Hijacking emergency granulopoiesis: Neutrophil ontogeny and reprogramming in cancer
Molecular Oncology, EarlyView.Neutrophils are highly plastic innate immune cells; their functions in cancer extend beyond the tumour microenvironment. This Review summarises current understanding of neutrophil maturation and heterogeneity and highlights tumour‐induced granulopoiesis as a systemic programme that expands immature, immunosuppressive neutrophils via tumour‐derived ...
Gabriela Marinescu, Yi Feng
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Multiple Transitivity of Primitive Permutation Groups [PDF]
Proceedings of the American Mathematical Society, 1965 Introduction. We wish to consider two theorems on permutation groups which are a generalization of a two-part theorem found in [1, pp. 66-67], a theorem concerned with a permutation group on a finite set. We shall remove the restriction of finiteness.
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