Results 11 to 20 of about 55,118 (252)
Primitive permutation groups with a regular subgroup
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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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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ON A CONJECTURE ON THE PERMUTATION CHARACTERS OF FINITE PRIMITIVE GROUPS
Bulletin of the Australian Mathematical Society, 2019 Let $G$ be a finite group with two primitive permutation representations on the sets $\unicode[STIX]{x1D6FA}_{1}$ and $\unicode[STIX]{x1D6FA}_{2}$ and let $\unicode[STIX]{x1D70B}_{1}$ and $\unicode[STIX]{x1D70B}_{2}$ be the corresponding permutation ...
Pablo Spiga
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On the degress of primitive permutation groups
Mathematische Zeitschrift, 1982 Peter Cameron +2 more
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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
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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
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On the number of conjugacy classes of a primitive permutation group [PDF]
Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2020 Let $G$ be a primitive permutation group of degree $n$ with nonabelian socle, and let $k(G)$ be the number of conjugacy classes of $G$. We prove that either $k(G)< n/2$ and $k(G)=o(n)$ as $n\rightarrow \infty$, or $G$ belongs to explicit families of ...
Daniele Garzoni, Nick Gill
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Base sizes of primitive permutation groups [PDF]
Monatshefte für Mathematik (Print), 2021 Let G be a permutation group, acting on a set Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin ...
Mariapia Moscatiello, C. Roney‐Dougal
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On Edge-Primitive Graphs of Order as a Product of Two Distinct Primes
Mathematics, 2023 A graph is edge-primitive if its automorphism group acts primitively on the edge set of the graph. Edge-primitive graphs form an important subclass of symmetric graphs. In this paper, edge-primitive graphs of order as a product of two distinct primes are
Renbing Xiao, Xiaojiao Zhang, Hua Zhang
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