NONABELIAN FULLY-RAMIFIED SECTIONS

Let G be a finite group and let K and L be normal subgroups of G such that \K : L\ and \G : K\ are relatively prime, and assume that \K : L\ is odd. Let H be a subgroup of G such that G = HK and H boolean AND K = L. Let phi be an irreducible character of L that is invariant under the action of H and is fully ramified with respect to K/L. If chi is an element of Irr(G) is a constituent of phi(G), then we prove that ch i(H) has a unique irreducible constituent having odd multiplicity.