Suppose that χ is an irreducible complex character of a finite group G and let fχ be the smallest integer n such that the cyclotomic field ℚn contains the values of χ. Let p be a prime, and assume that χ ∈ Irr(G) has degree not divisible by p. We show that if G is solvable and χ(1) is odd, then there exists g ∈ NG(P)/P′ with o(g) = fχ, where P ∈ Sylp(G). In particular, fχ divides |NG(P) : P′|.
Feit numbers and p′-degree characters / Vallejo Rodriguez C.. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 19:(2016), pp. 1129-1136. [10.1515/jgth-2016-0011]
Feit numbers and p′-degree characters
Vallejo Rodriguez C.
2016
Abstract
Suppose that χ is an irreducible complex character of a finite group G and let fχ be the smallest integer n such that the cyclotomic field ℚn contains the values of χ. Let p be a prime, and assume that χ ∈ Irr(G) has degree not divisible by p. We show that if G is solvable and χ(1) is odd, then there exists g ∈ NG(P)/P′ with o(g) = fχ, where P ∈ Sylp(G). In particular, fχ divides |NG(P) : P′|.
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