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Divisibility of degrees in McKay correspondences

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Abstract

If p is a prime and G is a finite solvable group, we prove that there is a McKay correspondence between the irreducible characters of G of degree not divisible by p and those of a p-Sylow normalizer of G which respects divisibility. This phenomenon does not happen outside solvable groups.

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Acknowledgements

I would like to thank E. Giannelli for very useful comments on this subject. Also, part of this work was done while the author stayed at the Mathematical Sciences Research Institute in Berkeley and I would like to thank MSRI for its hospitality.

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Correspondence to Noelia Rizo.

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This research is supported by Proyecto MTM2016-76196-P, and Fellowship FPU of Ministerio de Educación, Cultura y Deporte.

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Rizo, N. Divisibility of degrees in McKay correspondences. Arch. Math. 112, 5–11 (2019). https://doi.org/10.1007/s00013-018-1239-0

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  • DOI: https://doi.org/10.1007/s00013-018-1239-0

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