Search results for "Category"

showing 10 items of 4660 documents

Differential equations over polynomially bounded o-minimal structures

2002

We investigate the asymptotic behavior at +∞ of non-oscillatory solutions to differential equations y' = G(t, y), t > a, where G: R 1+l → R l is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled.

CombinatoricsDiscrete mathematicsAsymptotic analysisDifferential equationApplied MathematicsGeneral MathematicsBounded functionClosure (topology)Structure (category theory)PfaffianReal fieldMathematicsProceedings of the American Mathematical Society
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Hypergraph functor and attachment

2010

Using an arbitrary variety of algebras, the paper introduces a fuzzified version of the notion of attachment in a complete lattice of Guido, to provide a common framework for the concept of hypergraph functor considered by different authors in the literature. The new notion also gives rise to a category of variable-basis topological spaces which is a proper supercategory of the respective category of Rodabaugh.

CombinatoricsFiber functorClosed categoryFunctorArtificial IntelligenceLogicMathematics::Category TheoryConcrete categoryUniversal propertyCone (category theory)Variety (universal algebra)Topological spaceMathematicsFuzzy Sets and Systems
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p-Parts of Brauer character degrees

2014

Abstract Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.

CombinatoricsFinite groupAlgebra and Number TheoryCharacter (mathematics)Brauer's theorem on induced charactersSolvable groupStructure (category theory)Mathematics::Representation TheoryPrime (order theory)MathematicsJournal of Algebra
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A Dual Version of Huppert's  -  Conjecture

2010

Huppert’s ρ-σ conjecture asserts that any finite group has some character degree that is divisible by “many” primes. In this note, we consider a dual version of this problem, and we prove that for any finite group there is some prime that divides “many” character degrees.

CombinatoricsFinite groupConjectureCharacter (mathematics)Mathematics::Number TheoryGeneral MathematicsMathematics::Metric GeometryDegree (angle)Prime (order theory)Dual (category theory)MathematicsInternational Mathematics Research Notices
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On Join Properties of Hall π-Subgroups of Finite π-Soluble Groups

1998

All groups considered in the sequel are finite. K. Doerk and T. Hawkes, in Section I.4 of their recent comprehensive w x volume on finite soluble groups 1 , include background material and a proof of the following result: Let S be a Hall system of a soluble group G and let U and V be subgroups into which S reduces. Then S reduces into U l V, and if , in addition, U permutes with V, then S reduces into UV. It is clear that the second part of the above result holds equally well with a single Hall subgroup in place of a Hall system; in other words, if a Hall p-subgroup of G contains Hall p-subgroups of U and V and U permutes with V, then it also contains a Hall p-subgroup of UV.

CombinatoricsHall subgroupAlgebra and Number TheorySection (category theory)Group (mathematics)Join (sigma algebra)MathematicsJournal of Algebra
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Cotype 2 estimates for spaces of polynomials on sequence spaces

2002

We give asymptotically correct estimations for the cotype 2 constant C2(P(mXn)) ofthe spaceP(mXn) of allm-homogenous polynomials onXn, the span of the firstn sequencesek=(\gdkj)j in a Banach sequence spaceX. Applications to Minkowski, Orlicz and Lorentz sequence spaces are given.

CombinatoricsMathematics::Functional AnalysisSequencesymbols.namesakeSpan (category theory)General MathematicsLorentz transformationMinkowski spaceMathematics::Optimization and ControlsymbolsAlgebra over a fieldConstant (mathematics)Mathematics
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Finite groups with subgroups supersoluble or subnormal

2009

Abstract The aim of this paper is to study the structure of finite groups whose non-subnormal subgroups lie in some subclasses of the class of finite supersoluble groups.

CombinatoricsMathematics::Group TheoryClass (set theory)Algebra and Number TheoryGroup of Lie typeLocally finite groupStructure (category theory)CA-groupCycle graph (algebra)Finite groupsSupersoluble groupsSoluble groupsMathematicsJournal of Algebra
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Generalised norms in finite soluble groups

2014

Abstract We give a framework for a number of generalisations of Baerʼs norm that have appeared recently. For a class C of finite nilpotent groups we define the C -norm κ C ( G ) of a finite group G to be the intersection of the normalisers of the subgroups of G that are not in C . We show that those groups for which the C -norm is not hypercentral have a very restricted structure. The non-nilpotent groups G for which G = κ C ( G ) have been classified for some classes. We give a classification for nilpotent classes closed under subgroups, quotients and direct products of groups of coprime order and show the known classifications can be deduced from our classification.

CombinatoricsMathematics::Group TheoryNilpotentFinite groupAlgebra and Number TheoryCoprime integersNorm (group)Structure (category theory)Order (group theory)Nilpotent groupQuotientMathematicsJournal of Algebra
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Coding with traces

1994

We prove that the existence of a coding between two trace monoids is decidable for some families of trace monoids. Decidability heavily depends on the structure of the dependence graphs. The concept of coding is based on the new notion of strong morphism between trace monoids.

CombinatoricsMorphismlawMathematics::Category TheorySuffix treeCoding (social sciences)MathematicsDecidabilitylaw.invention
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Permutable products of supersoluble groups

2004

We investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups. We show that the supersoluble residual is nilpotent and the Fitting quotient group is metabelian. These results are consequences of our main theorem, which states that such a product is supersoluble when the intersection of the two factors is core-free in the group.

CombinatoricsNilpotentAlgebra and Number TheoryIntersectionGroup (mathematics)Product (mathematics)Structure (category theory)Permutable primeQuotient groupMathematicsJournal of Algebra
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