Divisibility of degrees in McKay correspondences
- 43 Downloads
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.
KeywordsThe McKay conjecture Divisibility of degrees Solvable groups
Mathematics Subject ClassificationPrimary 20D Secondary 20C15
Unable to display preview. Download preview PDF.
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.
- 5.Isaacs, I.M.: Finite Group Theory. Graduate Studies in Mathematics, vol. 92. AMS, Providence (2008)Google Scholar
- 8.Navarro, G.: Character Theory and the McKay Conjecture. Cambridge Studies in Advanced Mathematics, vol. 175. Cambrige (2018)Google Scholar
- 10.Navarro, I.P.: A Divisibility problem in the McKay Conjecture, arXiv:1711.00642