Let G be a finite group, let p be an odd prime, and let P Î Sylp(G). If NG(P) = PCG(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.
Mckay natural correspondences on characters / Navarro G.; Tiep P.H.; Vallejo C.. - In: ALGEBRA & NUMBER THEORY. - ISSN 1937-0652. - STAMPA. - 8:(2014), pp. 1839-1856. [10.2140/ant.2014.8.1839]
Mckay natural correspondences on characters
Vallejo C.
2014
Abstract
Let G be a finite group, let p be an odd prime, and let P Î Sylp(G). If NG(P) = PCG(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.
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