Search results for "Cyclotomic field"

showing 2 items of 2 documents

Brauer characters with cyclotomic field of values

2008

It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675–686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p=2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p≠q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q(exp(2πi/q)).

Pure mathematicsFinite groupBrauer's theorem on induced charactersCharacter (mathematics)Algebra and Number TheoryOrder (group theory)Composition (combinatorics)Mathematics::Representation TheoryCyclotomic fieldPrime (order theory)MathematicsJournal of Pure and Applied Algebra
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Characters of 𝑝’-degree with cyclotomic field of values

2006

If p p is a prime number and G G is a finite group, we show that G G has an irreducible complex character of degree not divisible by p p with values in the cyclotomic field Q p \mathbb {Q}_p .

Pure mathematicsFinite groupCharacter (mathematics)Degree (graph theory)Applied MathematicsGeneral MathematicsMathematicsofComputing_GENERALPrime numberCyclotomic fieldMathematicsProceedings of the American Mathematical Society
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