Navarro vertices and lifts in solvable groups

2023/02/20 by Lei Wang, Ping Jin, Wang, Lei +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2302.09698

openalex publication_date 2023/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Q be a p-subgroup of a finite p-solvable group G, where p is a prime, and suppose that δ is a linear character of Q with the property that δ(x)=δ(y) whenever x,y∈ Q are conjugate in G. In this situation, we show that restriction to p-regular elements defines a canonical bijection from the set of those irreducible ordinary characters of G with Navarro vertex (Q,δ) onto the set of irreducible Brauer characters of G with Green vertex Q. Also, we use this correspondence to examine the behavior of lifts of Brauer characters with respect to normal subgroups.

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