Vertices for irreducible characters of a class of blocks
By Charles Eaton
(preprint)
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. 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.