Primitive pairs of K-groups

In ‘Primitive pairs of $p$-solvable groups’, J. Algebra 324 (2010) 841-859, the author proved a non existence theorem for certain types of amalgams of $p$-solvable groups in the presence of operator groups acting coprimely on the groups in the amalgam. An application of that work was a new proof of the Solvable Signalizer Functor Theorem. In this article, the $p$-solvable restriction will be weakened to a $K$-group hypothesis. An application of this work will be a new proof of the Nonsolvable Signalizer Functor Theorem.