Results 31 to 40 of about 5,571,269 (248)

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., Praeger, Cheryl E., Saxl, Jan   +2 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., Aner Shalev, Cheryl E. Praeger, Praeger, CE, D. R. Heath-brown, Heath-Brown, David, Praeger, C. E., Shalev, A, Shalev, A., Heath-Brown, DR   +9 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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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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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, Liebeck, MW, Shalev, A, Liebeck, Martin W., Burness, Timothy C., Shalev, Aner   +5 more
core   +1 more source

On derangements in simple permutation groups

Forum of Mathematics, Sigma
Let $G \leqslant \mathrm {Sym}(\Omega )$ 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
doaj   +1 more source

Computing in permutation groups without memory [PDF]

, 2013
Funding: UK Engineering and Physical Sciences Research Council (EP/K033956/1)Memoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory.
Maximilien Gadouleau, Cameron, P., Gadouleau, Maximilien, Cameron, Peter Jephson, Gadouleau, M., Cameron, Peter, Fairbairn, Ben, Cameron, P.J., Peter J. Cameron, Ben Fairbairn, Gadoleau, M.   +10 more
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Separating subsets from their images

Forum of Mathematics, Sigma
Let G be a transitive permutation group acting on Ω $\Omega $ normal upper Omega . In this paper, we introduce and study the parameter sep(G) $\mathrm {sep}(G)$ sep left parenthesis upper G right parenthesis , which denotes the size of the ...
Marco Barbieri, Maruša Lekše, Primož Potočnik, Kamilla Rekvényi   +3 more
doaj   +1 more source

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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