Search results for "Order theory"

showing 10 items of 150 documents

Existentially closed central extensions of locally finite p-groups

1986

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

Discrete mathematicsClass (set theory)NoticeGeneral MathematicsAbelian groupPrime (order theory)MathematicsExistentially closed modelMathematical Proceedings of the Cambridge Philosophical Society
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Products of locally finite groups with min-p

1986

AbstractThe paper is devoted to showing that if the factorized group G = AB is almost solvable, if A and B are π-subgroups with min-p for some prime p in π and also if the hypercenter factor group A/H(A) or B/H(B) has min p for the prime p. then G is a π-group with min-p for the prime p.

Discrete mathematicsCombinatoricsGroup (mathematics)General MedicinePrime (order theory)MathematicsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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Basis-set completeness profiles in two dimensions

2002

A two-electron basis-set completeness profile is proposed by analogy with the one-electron profile introduced by D. P. Chong (Can J Chem 1995, 73, 79). It is defined as Y(alpha, beta) = sigmam sigman (Galpha(1)Gbeta(2)/(1/r12)/ psim(1)psin(2)) (psim(1)psin(2)/r12/Galpha(1)Gp(2)) and motivated by the expression for the basis-set truncation correction that occurs in the framework of explicitly correlated methods (Galpha is a scanning Gaussian-type orbital of exponent alpha and [psim] is the orthonormalized one-electron basis under study). The two-electron basis-set profiles provide a visual assessment of the suitability of basis sets to describe electron-correlation effects. Furthermore, they…

Discrete mathematicsComputational MathematicsAngular momentumBasis (linear algebra)TruncationCompleteness (order theory)ExponentGeneral ChemistryExpression (computer science)Linear subspaceBasis setMathematicsJournal of Computational Chemistry
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NP-completeness of the hamming salesman problem

1985

It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.

Discrete mathematicsComputer Networks and CommunicationsApplied MathematicsComputer Science::Neural and Evolutionary ComputationHamming distanceComputer Science::Computational ComplexityTravelling salesman problemCombinatoricsHigh Energy Physics::TheoryComputational MathematicsCompleteness (order theory)Computer Science::Data Structures and AlgorithmsNP-completeBottleneck traveling salesman problemHamming codeSoftwareComputer Science::Information TheoryMathematicsBIT
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Introduction to generalized topological spaces

2011

[EN] We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.

Discrete mathematicsConnected spaceCompatible ideallcsh:Mathematicslcsh:QA299.6-433lcsh:AnalysisTopological spacelcsh:QA1-939Order generated by idealTopological vector spaceSeparation axiomSeparated setsModulo idealEmbeddingIdeal (order theory)FrameGeometry and TopologyGeneral topologyGeneralized topological spaceGeneralized topologyMathematicsgt-space
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p-Length andp′-Degree Irreducible Characters Having Values in ℚp

2013

Let G be a p-solvable group of p-length l, where p is any prime. We show that G has at least 2 l irreducible characters of degree coprime to p and having values inside ℚ p . This generalizes a previous result for p = 2 [6] to arbitrary primes. With the same notation, we prove that if p is odd then G has at least 2 l Galois orbits of conjugacy classes of p-elements having values in ℚ p .

Discrete mathematicsFinite groupAlgebra and Number TheoryConjugacy classDegree (graph theory)Coprime integersGroup (mathematics)Mathematics::Number TheoryPrime (order theory)MathematicsCommunications in Algebra
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McKay natural correspondences on characters

2014

Let [math] be a finite group, let [math] be an odd prime, and let [math] . If [math] , then there is a canonical correspondence between the irreducible complex characters of [math] of degree not divisible by [math] belonging to the principal block of [math] and the linear characters of [math] . As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow [math] -subgroup or a [math] -decomposable Sylow normalizer.

Discrete mathematicsFinite groupAlgebra and Number TheoryDegree (graph theory)self-normalizing Sylow subgroup20C15Sylow theoremsBlock (permutation group theory)Characterization (mathematics)Centralizer and normalizerPrime (order theory)$p$-decomposable Sylow normalizerCombinatoricsMathematics::Group TheoryMcKay conjecture20C20MathematicsAlgebra & Number Theory
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Quadratic rational solvable groups

2012

Abstract A finite group G is quadratic rational if all its irreducible characters are either rational or quadratic. If G is a quadratic rational solvable group, we show that the prime divisors of | G | lie in { 2 , 3 , 5 , 7 , 13 } , and no prime can be removed from this list. More generally, if G is solvable and the field Q ( χ ) generated by the values of χ over Q satisfies | Q ( χ ) : Q | ⩽ k , for all χ ∈ Irr ( G ) , then the set of prime divisors of | G | is bounded in terms of k . Also, we prove that the degree of the field generated by the values of all characters of a semi-rational solvable group (see Chillag and Dolfi, 2010 [1] ) or a quadratic rational solvable group over Q is bou…

Discrete mathematicsFinite groupAlgebra and Number TheoryField (mathematics)Isotropic quadratic formPrime (order theory)CombinatoricsQuadratic equationSolvable groupSolvable groupRational characterBounded functionQuadratic fieldQuadratic fieldMathematicsJournal of Algebra
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A note on a result of Guo and Isaacs about p-supersolubility of finite groups

2016

In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to . We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing such that , if is S-semipermutable in for all normal subgroups H of P with , then either G is p-supersoluble or else . This extends the main result of Guo and Isaacs in (Arch. Math. 105:215-222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups.

Discrete mathematicsFinite groupCoprime integersP-supersoluble groupGeneral MathematicsS-semipermutable subgroup010102 general mathematicsSylow theoremsGrups Teoria deOrder (ring theory)01 natural sciencesPrime (order theory)CombinatoricsGlobal informationLocally finite group0103 physical sciences010307 mathematical physicsFinite group0101 mathematicsMATEMATICA APLICADAMatemàticaMathematicsArchiv der Mathematik
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Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time

2002

This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and mac…

Discrete mathematicsGeneral Computer ScienceUnary operationGeneral Mathematics[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Recursion (computer science)[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]0102 computer and information sciences02 engineering and technologyFunction (mathematics)01 natural sciencesRandom-access machine010201 computation theory & mathematicsCompleteness (order theory)0202 electrical engineering electronic engineering information engineeringComplexity class020201 artificial intelligence & image processingAlgebraic numberTime complexityMathematics
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