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- W1981523910 abstract "Let G be a finite solvable group, p be some prime, let P be a Sylow p -subgroup of G , and let N be its normalizer in G . Assume that N has odd order. Then, we prove that there exists a bijection from the set of all irreducible characters of G of degree prime to p to the set of all the irreducible characters of degree prime to p of N such that it preserves ± the degree modulo p , the field of values, and the Schur index over every field of characteristic zero. This strengthens a more general recent result [A. Turull, Character correspondences in solvable groups, J. Algebra 295 (2006) 157–178], but only for the case under consideration here. In addition, we prove some other strong character correspondences that have very good rationality properties. As one consequence, we prove that a solvable group G has a non-trivial rational irreducible character with degree prime to p if and only if the order of the normalizer of a Sylow p -subgroup of G has even order." @default.
- W1981523910 created "2016-06-24" @default.
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- W1981523910 date "2008-01-01" @default.
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- W1981523910 title "Odd character correspondences in solvable groups" @default.
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- W1981523910 doi "https://doi.org/10.1016/j.jalgebra.2006.02.042" @default.
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