Character degrees and local subgroups revisited

2024/11/24 by Jorge Martínez, Martínez, J. Miquel
Engineering · Mathematics · #20C15 #20C20 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2411.15968

openalex publication_date 2024/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p and q be different primes and let G be a finite q-solvable group. We prove that Irr_p'(G)⊆ Irr_q'(G) if and only if N_G(P)⊆ N_G(Q) and C_Q'(P)=1 for some P\inSyl_p(G) and Q\inSyl_q(G). Further, if B is a q-block of G and p does not divide the degree of any character in Irr(B) then we prove that a Sylow p-subgroup of G is normalized by a defect group of B. This removes the p-solvability condition of two theorems of G. Navarro and T. R. Wolf.

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