# Vertices for irreducible characters of a class of blocks

Eaton, Charles W. (2005) Vertices for irreducible characters of a class of blocks. Journal of Algebra, 286 (2). pp. 492-499. ISSN 0021-8693

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, 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.