Navarro vertices and lifts in solvable groups

Abstract

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