On almost p -rational characters in principal blocks
Maróti, Attila (Hun-Ren Alfred Renyi Institute of Mathematics (Budapest, Hongria))
Martínez Marín, Josep Miquel (Universitat de València. Departament de Matemàtiques)
Schaeffer Fry, A. A. (University of Denver. Department of Mathematics)
Vallejo, Carolina (Università degli Studi di Firenze. Dipartamento di Matematica e Informatica 'Ulisse Dini')

Data:	2026
Resum:	Let p be a prime. In this paper we provide a lower bound for the number of almost p-rational characters of degree coprime to p in the principal p-block of a finite group of order divisible by p. We further describe the p-local structure of the groups for which the above-mentioned bound is sharp.
Nota:	The first-named author was supported by the National Research, Development and Innovation Office (NKFIH) Grant no. K138596, no. K132951, and Grant no. K138828. The second-named author is funded by the national project PRIN 2022-2022PSTWLB-Group Theory and Applications-CUP B53D23009410006. The third-named author gratefully acknowledges support from the U.S. National Science Foundation, Award nos. DMS-2100912 and DMS-2439897, and thanks her former institution, Metropolitan State University of Denver, which held the former and allowed her to serve as PI. The fourth-named author, as part of the GNSAGA, is grateful for the support of the Istituto Nazionale di Alta Matematica (INdAM). She also acknowledges support from the Rita Levi-Montalcini Programme 2019. Part of this work was carried out while the second-named author visited the University of Florence during the fall of 2023, funded by a Borsa Ferran Sunyer i Balaguer 2023 from l'Institut d'Estudis Catalans.
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Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Galois action on characters ; Principal blocks ; Height zero character
Publicat a:	Publicacions matemàtiques, Vol. 70, Num. 1 (2026) , p. 55-78 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/980000003199
DOI: 10.5565/PUBLMAT7012603

24 p, 1.1 MB

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