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Degrees and p ‐rational characters
Author(s) -
Navarro Gabriel,
Tiep Pham Huu
Publication year - 2012
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds054
Subject(s) - sylow theorems , mathematics , character (mathematics) , finite group , normal subgroup , prime (order theory) , combinatorics , character table , degree (music) , pure mathematics , group (periodic table) , zero (linguistics) , discrete mathematics , geometry , linguistics , chemistry , physics , organic chemistry , philosophy , acoustics
Suppose that G is a finite group and that p is a prime number. We prove that if every p ‐rational irreducible character of G is non‐zero on every p ‐element of G , then G has a normal Sylow p ‐subgroup. This yields a p ‐rational refinement of the Itô–Michler theorem: if p does not divide the degree of any irreducible p ‐rational character of G , then G has a normal Sylow p ‐subgroup