  Let $A$ be an elementary abelian $r$-group with rank at least $3$ that acts
faithfully on the finite $r'$-group $G$. Assume that $G$ is $A$-simple, so that
$G = K_{1} \times\cdots\times K_{n}$ where $K_{1},\ldots,K_{n}$ is a collection
of simple subgroups of $G$ that is permuted transitively by $A$. The purpose of
this paper is to characterize $G$ and the collection of fixed point subgroups
$\{ C_{G}(a) \;|\; a \in A^{\#} \}$. An application of this result will be a
new proof of McBride's Nonsolvable Signalizer Functor Theorem.
