Search results for "rete"

showing 10 items of 3470 documents

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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On the supersoluble hypercentre of a finite group

2016

[EN] We give some sufficient conditions for a normal p-subgroup P of a finite group G to have every G-chief factor below it cyclic. The S-permutability of some p-subgroups of O^p(G)plays an important role. Some known results can be reproved and some others appear as corollaries of our main theorems.

Discrete mathematicsFinite groupP-supersoluble groupGeneral MathematicsS-semipermutable subgroup010102 general mathematicsGrups Teoria de01 natural sciencesMathematics::Group Theory0103 physical sciences010307 mathematical physicsFinite group0101 mathematicsMATEMATICA APLICADAMatemàticaMathematicsMonatshefte für Mathematik
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On self-normalising subgroups of finite groups

2010

[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively.

Discrete mathematicsFinite groupPst-groupAlgebra and Number TheoryMathematics::CombinatoricsGrups Teoria deAlgebraMathematics::Group TheoryT-groupPt-groupT-groupPermutabilitySylow permutabilityÀlgebraAlgebra over a fieldFinite groupPermutable closureSubnormal closureMATEMATICA APLICADAGroup theoryMathematics
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On the orders of zeros of irreducible characters

2009

Let G be a finite group and p a prime number. We say that an element g in G is a vanishing element of G if there exists an irreducible character χ of G such that χ (g) = 0. The main result of this paper shows that, if G does not have any vanishing element of p-power order, then G has a normal Sylow p-subgroup. Also, we prove that this result is a generalization of some classical theorems in Character Theory of finite groups. © 2008 Elsevier Inc. All rights reserved.

Discrete mathematicsFinite groupPure mathematicsBrauer's theorem on induced charactersAlgebra and Number Theoryirreducible character zeroCharacter theorySylow theoremsPrime numberIrreducible elementFinite groupsCharacter (mathematics)Order (group theory)Zeros of charactersCharactersMathematics
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Inducing characters and nilpotent subgroups

1996

If H H is a subgroup of a finite group G G and γ ∈ Irr ⁡ ( H ) \gamma \in \operatorname {Irr}(H) induces irreducibly up to G G , we prove that, under certain odd hypothesis, F ( G ) F ( H ) \mathbf {F}(G) \mathbf {F}(H) is a nilpotent subgroup of G G .

Discrete mathematicsFinite groupPure mathematicsNilpotentApplied MathematicsGeneral MathematicsMathematics
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On a graph related to permutability in finite groups

2010

For a finite group G we define the graph $\Gamma(G)$ to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes $\{\mathcal {A}, \mathcal {B}\}$ are joined by an edge if for some $\{A \in \mathcal {A},\, B \in \mathcal {B}\, A\}$ and B permute. We characterise those groups G for which $\Gamma(G)$ is complete.

Discrete mathematicsFinite groupSoluble groupApplied MathematicsGrups Teoria deGraphGraphCombinatoricsMathematics::Group TheoryConjugacy classPermutabilityÀlgebraFinite groupMATEMATICA APLICADAMathematics
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Finite State Verifiers with Constant Randomness

2012

We give a new characterization of NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers.

Discrete mathematicsFinite-state machine010102 general mathematics0102 computer and information sciencesGas meter prover01 natural sciencesRegular language010201 computation theory & mathematicsBounded functionProbabilistic automaton0101 mathematicsConstant (mathematics)Time complexityRandomnessMathematics
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On a Conjecture by Christian Choffrut

2017

It is one of the most famous open problems to determine the minimum amount of states required by a deterministic finite automaton to distinguish a pair of strings, which was stated by Christian Choffrut more than thirty years ago. We investigate the same question for different automata models and we obtain new upper and lower bounds for some of them including alternating, ultrametric, quantum, and affine finite automata.

Discrete mathematicsFinite-state machineConjecture010102 general mathematics02 engineering and technology01 natural sciencesUpper and lower boundsAutomatonDeterministic finite automatonCounting problem0202 electrical engineering electronic engineering information engineeringComputer Science (miscellaneous)020201 artificial intelligence & image processingAffine transformation0101 mathematicsUltrametric spaceMathematicsInternational Journal of Foundations of Computer Science
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Team learning as a game

1997

A machine FIN-learning machine M receives successive values of the function f it is learning; at some point M outputs conjecture which should be a correct index of f. When n machines simultaneously learn the same function f and at least k of these machines outut correct indices of f, we have team learning [k,n]FIN. Papers [DKV92, DK96] show that sometimes a team or a robabilistic learner can simulate another one, if its probability p (or team success ratio k/n) is close enough. On the other hand, there are critical ratios which mae simulation o FIN(p2) by FIN(p1) imossible whenever p2 _< r < p1 or some critical ratio r. Accordingly to [DKV92] the critical ratio closest to 1/2 rom the let is…

Discrete mathematicsFinite-state machineConjectureTeam learningAlgorithm complexityFunction (mathematics)Critical ratioAlgorithmMathematics
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Nondeterministic operations on finite relational structures

1998

Abstract This article builds on a tutorial introduction to universal algebra for language theory (Courcelle, Theoret. Comput. Sci. 163 (1996) 1–54) and extends it in two directions. First, nondeterministic operations are considered, i.e., operations which give a set of results instead of a single one. Most of their properties concerning recognizability and equational definability carry over from the ordinary case with minor modifications. Second, inductive sets of evaluations are studied in greater detail. It seems that they are handled most naturally in the framework presented here. We consider the analogues of top-down and bottom-up tree transducers. Again, most of their closure propertie…

Discrete mathematicsFinite-state machineGeneral Computer ScienceComputer scienceLogicFormal languages (recognizable and context-free sets transducers)Unbounded nondeterminismMonad (functional programming)Symbolic computationHypergraphsFirst-order logicLogical theoryDecidabilityTheoretical Computer ScienceNondeterministic algorithmAlgebraDeterministic automatonFormal languageUniversal algebraEquivalence relationTree transducersRewritingComputer Science(all)Theoretical Computer Science
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