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arXiv · 2204.10124

Degree divisibility in Alperin-McKay correspondences

J. Miquel Martìnez·Damiano Rossi
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Abstract

Let p be a prime, B a p-block of a finite group G and b its Brauer correspondent. According to the Alperin-McKay Conjecture, there exists a bijection between the set of irreducible ordinary characters of height zero of B and those of b. In this paper, we show that whenever G is p-solvable such a bijection can be found, both for ordinary and Brauer characters, with the additional property of being compatible with divisibility of character degrees. In this case, we also show that the dimension of b divides the dimension of B.

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BibTeXRIS

J. Miquel Martìnez, Damiano Rossi. 2022-04-21. Degree divisibility in Alperin-McKay correspondences. https://arxiv.org/abs/2204.10124

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