On normal subgroups and simple modules with a given vertex in a p-solvable group

Abstract: Let N be a normal subgroup of a p-solvable group G and let M be a simple FN-module, where F is an algebraically closed field of characteristic p. Let Q be any p-subgroup of G. In this paper, we count the number of simple FG-modules lying over M and having Q as a vertex. [Copyright &y& Elsevier]