Search results for "Rational character"

showing 4 items of 4 documents

Rationality and normal 2-complements

2008

Abstract We study the finite groups in which every irreducible rational valued character is linear, and those in which every rational element is central.

AlgebraCharacter (mathematics)Algebra and Number TheoryRational pointRationalityRational classesRational functionElement (category theory)Rational charactersMathematicsJournal of Algebra
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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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Degrees of rational characters of finite groups

2010

Abstract A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result.

Finite groupMathematics(all)Brauer's theorem on induced charactersGeneral Mathematics010102 general mathematics01 natural sciencesPrime (order theory)CombinatoricsNormal p-complementCharacter (mathematics)Rational characterNormal p-complement0103 physical sciencesDegree (angle)010307 mathematical physics0101 mathematicsClassical theoremMathematicsAdvances in Mathematics
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Characterization of rhenium oxide films and their application to liquid crystal cells

2009

Rhenium trioxide exhibits high electronic conductivity, while its open cubic crystal structure allows an appreciable hydrogen intercalation, generating disordered solid phases, with protonic conductivity. Rhenium oxide thin films have been obtained by thermal evaporation of ReO3 powders on different substrates, maintained at different temperatures, and also by reactive magnetron sputtering of a Re metallic target. A comparative investigation has been carried out on these films, by using micro-Raman spectroscopy and x-ray diffraction. Two basic types of solid phases appear to grow in the films: a red metallic HxReO3 compound, with distorted perovskite structures, like in the bulk material, a…

structural and vibrational characterizationMaterials sciencePerrhenateInorganic chemistryGeneral Physics and Astronomychemistry.chemical_elementCrystal structureSputter depositionRheniumIndium tin oxidechemistry.chemical_compoundRhenium trioxidechemistryChemical engineeringLiquid crystalRhenium oxide filmsRhenium oxide films; structural and vibrational characterization; electro-optic response.electro-optic responsePerovskite (structure)Journal of Applied Physics
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