TY - JOUR
T1 - p-rational characters and self-normalizing sylowp-subgroups
AU - Navarro, Gabriel
AU - Tiep, Phamhuu
AU - Turull, Alexandre
PY - 2007/4/19
Y1 - 2007/4/19
N2 - Let G be a finite group, p a prime, and P a Sylow p-subgroup of G. Several recent refinements of the McKay conjecture suggest that there should exist a bijection between the irreducible characters of pʹ-degree of G and the irreducible characters of pʹ-degree of NG(P), which preserves field of values of correspondent characters (over the p-adics). This strengthening of the McKay conjecture has several consequences. In this paper we prove one of these consequences: If p 2, then G has no non-trivial pʹ-degree p-rational irreducible characters if and only if NG(P) = P.
AB - Let G be a finite group, p a prime, and P a Sylow p-subgroup of G. Several recent refinements of the McKay conjecture suggest that there should exist a bijection between the irreducible characters of pʹ-degree of G and the irreducible characters of pʹ-degree of NG(P), which preserves field of values of correspondent characters (over the p-adics). This strengthening of the McKay conjecture has several consequences. In this paper we prove one of these consequences: If p 2, then G has no non-trivial pʹ-degree p-rational irreducible characters if and only if NG(P) = P.
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U2 - 10.1090/S1088-4165-07-00263-4
DO - 10.1090/S1088-4165-07-00263-4
M3 - Article
AN - SCOPUS:54149096927
SN - 1088-4165
VL - 11
SP - 84
EP - 94
JO - Representation Theory
JF - Representation Theory
IS - 4
ER -