Search results for "Group Theory"

showing 10 items of 703 documents

Maximal subgroups of small index of finite almost simple groups

2022

We prove in this paper that a finite almost simple group $R$ with socle the non-abelian simple group $S$ possesses a conjugacy class of core-free maximal subgroups whose index coincides with the smallest index $\operatorname{l}(S)$ of a maximal group of $S$ or a conjugacy class of core-free maximal subgroups with a fixed index $v_S \leq {\operatorname{l}(S)^2}$, depending only on $S$. We show that the number of subgroups of the outer automorphism group of $S$ is bounded by $\log^3 {\operatorname{l}(S)}$ and $\operatorname{l}(S)^2 < |S|$.

Computational MathematicsMathematics::Group Theory20E28 20E32 20B15Algebra and Number TheoryMathematics::ProbabilityApplied MathematicsFOS: MathematicsGeometry and TopologyGroup Theory (math.GR)Mathematics::Representation TheoryMatemàticaMathematics - Group TheoryAnalysis
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Rational solutions to the KPI equation from particular polynomials

2022

Abstract We construct solutions to the Kadomtsev–Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second spatial derivative of a logarithm of a determinant of order n . We obtain with this method an infinite hierarchy of rational solutions to the KPI equation. We give explicitly the expressions of these solutions for the first five orders.

Computational MathematicsNonlinear Sciences::Exactly Solvable and Integrable SystemsLogarithmHierarchy (mathematics)Applied MathematicsModeling and SimulationGeneral Physics and AstronomyOrder (group theory)Applied mathematicsHigh Energy Physics::ExperimentDerivativeA determinantMathematicsWave Motion
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Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le ca…

1999

Consider a sub-riemannian geometry (U,D,g) where U is a neighborhood of 0 in R 3 , D is a Martinet type distribution identified to ker ω , ω being the 1-form: , q=(x,y,z) and g is a metric on D which can be taken in the normal form : , a=1+yF(q) , c=1+G(q) , . In a previous article we analyze the flat case : a=c=1 ; we describe the conjugate and cut loci , the sphere and the wave front . The objectif of this article is to provide a geometric and computational framework to analyze the general case. This frame is obtained by analysing three one parameter deformations of the flat case which clarify the role of the three parameters in the gradated normal form of order 0 where: , . More generall…

Computational MathematicsPure mathematicsControl and OptimizationControl and Systems EngineeringOrder (group theory)GeometryType distributionMathematicsESAIM: Control, Optimisation and Calculus of Variations
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Gray visiting Motzkins

2002

We present the first Gray code for Motzkin words and their generalizations: k colored Motzkin words and Schroder words. The construction of these Gray codes is based on the observation that a k colored Motzkin word is the shuffle of a Dyck word by a k-ary variation on a trajectory which is a combination. In the final part of the paper we give some algorithmic considerations and other possible applications of the techniques introduced here.

Computer Networks and CommunicationsGeneralizationComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONCombinatoricsGray codeColoredAlgorithmicsMotzkin numberCode (cryptography)ArithmeticGray (horse)SoftwareWord (group theory)Information SystemsMathematicsActa Informatica
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Rational irreducible characters and rational conjugacy classes in finite groups

2007

We prove that a finite group G G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree.

Computer Science::Machine LearningFinite groupApplied MathematicsGeneral MathematicsIrreducible elementComputer Science::Digital LibrariesIrreducible fractionCombinatoricsStatistics::Machine LearningConjugacy classCharacter (mathematics)Character tableComputer Science::Mathematical SoftwareOrder (group theory)Character groupMathematicsTransactions of the American Mathematical Society
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Some subgroup embeddings in finite groups: A mini review

2015

[EN] In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied. ª 2014 Production and hosting by Elsevier B.V. on behalf of Cairo University

Computer scienceMini Reviewmacromolecular substancesS-permutabilityMini reviewMathematics::Group TheoryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONPermutabilityPrimitive subgroupAlgebra over a fieldFinite grouplcsh:Science (General)GeneralFinite grouplcsh:R5-920MultidisciplinaryMathematics::Combinatoricsmusculoskeletal neural and ocular physiologyAlgebranervous systemEmbeddingQuasipermutable subgrouplcsh:Medicine (General)MATEMATICA APLICADAAlgorithmSemipermutabilityMathematicsofComputing_DISCRETEMATHEMATICSlcsh:Q1-390Journal of Advanced Research
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Method for determining the proper expansion center and order for Mellin radial harmonic filters

1993

Abstract A method to improve the behaviour of the Mellin radial harmonic (MRH) filters in scale invariant pattern recognition is presented. An algorithm has been introduced to obtain the proper expansion center and order of the MRH development of any object. The procedure consists of the suspression of the non-discriminant uniform background in the energy function of the target. Computer simulations are presented.

Computer sciencebusiness.industryOrder (ring theory)Function (mathematics)Center (group theory)Scale invarianceAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsOpticsPattern recognition (psychology)HarmonicDevelopment (differential geometry)Electrical and Electronic EngineeringPhysical and Theoretical ChemistrybusinessEnergy (signal processing)Optics Communications
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Commensurability classification of a family of right-angled Coxeter groups

2008

We classify the members of an infinite family of right-angled Coxeter groups up to abstract commensurability.

Condensed Matter::Quantum GasesPure mathematicsApplied MathematicsGeneral MathematicsCoxeter groupPoint groupCommensurability (mathematics)AlgebraMathematics::Group TheoryCoxeter complexArtin groupCondensed Matter::Strongly Correlated ElectronsMathematics::Representation TheoryCoxeter elementMathematicsProceedings of the American Mathematical Society
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Glass transitions and scaling laws within an alternative mode-coupling theory

2015

Idealized glass transitions are discussed within an alternative mode-coupling theory (TMCT) proposed by Tokuyama [Physica A 395, 31 (2014)]. This is done in order to identify common ground with and differences from the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the corre…

Condensed Matter::Soft Condensed MatterScaling lawTheoretical physicsStatistical Mechanics (cond-mat.stat-mech)Mode couplingFOS: Physical sciencesOrder (group theory)Gravitational singularityDisordered Systems and Neural Networks (cond-mat.dis-nn)Schematic modelCondensed Matter - Disordered Systems and Neural NetworksCondensed Matter - Statistical MechanicsMathematics
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2-Groups with few rational conjugacy classes

2011

Abstract In this paper we prove the following conjecture of G. Navarro: if G is a finite 2-group with exactly 5 rational conjugacy classes, then G is dihedral, semidihedral or generalized quaternion. We also characterize the 2-groups with 4 rational classes.

Conjugacy classesDiscrete mathematicsMathematics::Group TheoryPure mathematicsConjectureConjugacy classAlgebra and Number TheoryDihedral angleQuaternion2-GroupsMathematicsJournal of Algebra
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