  A permutation group $(X,G)$ is said to be binary, or of relational complexity
$2$, if for all $n$, the orbits of $G$ (acting diagonally) on $X^2$ determine
the orbits of $G$ on $X^n$ in the following sense: for all $\bar{x},\bar{y} \in
X^n$, $\bar{x}$ and $\bar{y}$ are $G$-conjugate if and only if every pair of
entries from $\bar{x}$ is $G$-conjugate to the corresponding pair from
$\bar{y}$. Cherlin has conjectured that the only finite primitive binary
permutation groups are $S_n$, groups of prime order, and affine orthogonal
groups $V\rtimes O(V)$ where $V$ is a vector space equipped with an anisotropic
quadratic form; recently he succeeded in establishing the conjecture for those
groups with an abelian socle. In this note, we show that what remains of the
conjecture reduces, via the O'Nan-Scott Theorem, to groups with a nonabelian
simple socle.
