Results 1 to 10 of about 55,019 (153)
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
doaj +3 more sources
Primitive permutation IBIS groups [PDF]
Journal of Combinatorial Theory, Series A, 2021 Let $G$ be a finite permutation group on $\Omega$. An ordered sequence of elements of $\Omega$, $(\omega_1,\dots, \omega_t)$, is an irredundant base for $G$ if the pointwise stabilizer $G_{(\omega_1,\dots, \omega_t)}$ is trivial and no point is fixed by ...
A. Lucchini +2 more
semanticscholar +7 more sources
On the point stabilizer in a primitive permutation group
Mathematische Zeitschrift, 1973 Wolfgang Knapp, Knapp Wolfgang
exaly +3 more sources
Pre-primitive permutation groups [PDF]
Journal of Algebra, 2023 A transitive permutation group $G$ on a finite set $\Omega$ is said to be pre-primitive if every $G$-invariant partition of $\Omega$ is the orbit partition of a subgroup of $G$.
Marina Anagnostopoulou-Merkouri +2 more
semanticscholar +5 more sources
Sync-Maximal Permutation Groups Equal Primitive Permutation Groups [PDF]
Workshop on Descriptional Complexity of Formal Systems, 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 ...
Stefan Hoffmann
semanticscholar +3 more sources
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 \(n\).
R. Guralnick, K. Magaard
semanticscholar +3 more sources
Normalizers of Primitive Permutation Groups [PDF]
Advances in Mathematics, 2016 Let $G$ be a transitive normal subgroup of a permutation group $A$ of finite degree $n$. The factor group $A/G$ can be considered as a certain Galois group and one would like to bound its size.
R. Guralnick, Attila Mar'oti, L. Pyber
semanticscholar +4 more sources
Minimal degree, base size, order: selected topics on primitive permutation groups
Archiv Der Mathematik, 2023 In this survey article, we discuss the minimal degree, the base size, and the order of a finite primitive permutation group, along the lines of an article by Martin W. Liebeck.
Attila Maroti
exaly +2 more sources
Computation of Polya Polynomials of Primitive Permutation Group [PDF]
Mathematics of Computation, 1981 An almost complete list of Pólya polynomials of all primitive permutation groups up to degree 20 has been computed. The number-theoretical interpretation of Pólya polynomials and van der Waerden’s test make this a good tool to find safe conjectures for determining the group of an equation. This work was encouraged and supported by Professor W.
R. Land
semanticscholar +2 more sources
On the Base Size and Rank of a Primitive Permutation Group
Journal of Algebra, 1997 In this note, we relate the size of a base for a primitive permutation group to its rank with a character-theoretic proof of an elementary general bound.
G. Robinson
semanticscholar +2 more sources