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.