A new generalization of the McKay conjecture for p-solvable groups

2025/12/08 by Chang, Huimin, Jin, Ping
#20C15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2512.07073

Abstract

Let P be a Sylow p-subgroup of a finite p-solvable group G, where p is a prime. Using a normal p-series N of G, we introduce the notion of (N,p)-stable characters and prove that G and \bf N_G(P) have equal numbers of such characters, which gives a new generalization of the McKay conjecture for p-solvable groups. Also, we establish a canonical bijection between these characters in the case where G has odd order. Our proofs heavily depend on the theory of self-stabilizing pairs developed by M. L. Lewis, as well as some results of p-special characters due to I. M. Isaacs.

Citations

• Lifts of partial characters with respect to a chain of normal subgroups

Related

• The McKay conjecture with coprime group automorphisms and the Okuyama-Wajima argument
• New refinements of the McKay conjecture for arbitrary finite groups
• Character correspondeces in solvable groups with a self-normalizing Sylow subgroup
• The McKay Conjecture on character degrees
• Character Values of p-solvable groups on picky elements