Vertices for irreducible characters of a class of blocks

We observe that Navarro's definition of a vertex for an irreducible character of a p-solvable group may be extended to irreducible characters in p-blocks with defect groups contained in a normal p-solvable subgroup N, and show that this definition is independent of the choice of N. We show that the fundamental properties of Navarro's vertices generalize, and as a corollary show that the vertices of the irreducible Brauer characters in blocks of the above form are radical and are intersections of pairs of Sylow p-subgroups. © 2005 Elsevier Inc. All rights reserved.