2019/09/07 by Carolina Vallejo, Vallejo, Carolina
Computer Science · Engineering · Mathematics · #20C15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1909.03295
openalex publication_date 2019/09/07 · openalex created_date 2019/09/12 · openalex updated_date 2026/07/28
In 1973, I. M. Isaacs described a correspondence between characters of degree not divisible by a fixed prime p of a finite solvable group G and those of the normalizer of Sylow p-subgroup of G, whenever the index of the normalizer in G is odd. This correspondence is natural in the sense that an algorithm is provided to compute it, and the result of the application of the algorithm does not depend on choices made. Later on, for p-solvable groups with self-normalizing Sylow p-subgroup, G. Navarro showed that every irreducible character of degree not divisible by p has a unique linear constituent when restricted to a Sylow p-subgroup. Furthermore, the process of choosing the unique linear constituent of the restriction defines a bijection. Navarro's bijection is obviously natural in the sense described above. We show that these two correspondences are the same under the intersection of the hypotheses.