Results 11 to 20 of about 9,212,172 (248)
Prime order derangements in primitive permutation groups [PDF]
Journal of Algebra, 2011 It is an easy exercise that any transitive permutation group \(G\) on a set \(\Omega\), \(|\Omega|\geq 2\), contains an element, which acts fixed point freely. These elements are called derangements. A much deeper result, using the classification of the finite simple groups, due to \textit{B. Fein}, \textit{W. M. Kantor} and \textit{M.
Timothy C Burness
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Primitive permutation groups with a regular subgroup [PDF]
Journal of Algebra, 2007 In the present paper all triples \((G,\Omega,X)\) are determined where \(G\) is a primitive permutation group acting on a finite set \(\Omega\) and containing a regular subgroup \(X\) in the case that the socle \(\text{soc}(G)\) of \(G\) is alternating, sporadic or an exceptional group of Lie type. Many further examples \((G,\Omega,X)\) are constructed
Barbara Baumeister
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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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On the Minimal Degree of a Primitive Permutation Group [PDF]
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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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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On the degress of primitive permutation groups
Mathematische Zeitschrift, 1982 Peter Cameron
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Some codes and designs invariant under the groups $S_7$ and $S_8$ [PDF]
Journal of Mahani Mathematical Research, 2023 We use the Key-Moori Method 1 and examine 1-designs and codes from the representations of the alternating group $A_7$. It is shown that a self-dual symmetric 2-$(35,18,9)$ design and an optimal even binary $[21,14,4]$ LCD code are found such that they ...
Reza Kahkeshani
doaj +1 more source
Symmetric $1$-designs from $PSL_{2}(q),$ for $q$ a power of an odd prime [PDF]
Transactions on Combinatorics, 2021 Let $G = \PSL_{2}(q)$, where $q$ is a power of an odd prime. Let $M$ be a maximal subgroup of $G$. Define $\left\lbrace \frac{|M|}{|M \cap M^g|}: g \in G \right\rbrace$ to be the set of orbit lengths of the primitive action of $G$ on the ...
Xavier Mbaale, Bernardo Rodrigues
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Designs from maximal subgroups and conjugacy classes of $\mathrm{PSL}(2,q)$, $q$ odd [PDF]
AUT Journal of Mathematics and Computing, 2023 In this paper, using a method of construction of $1$-designs which are not necessarily symmetric, introduced by Key and Moori, we determine a number of $1$-designs with interesting parameters from the maximal subgroups and the conjugacy classes of ...
Xavier Mbaale +2 more
doaj +1 more source
On the point stabilizer in a primitive permutation group
Mathematische Zeitschrift, 1973 Wolfgang Knapp
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