  We develop local stable group theory directly from topological dynamics, and
extend the main results in this subject to the setting of stability "in a
model". Specifically, given a group $G$, we analyze the structure of sets
$A\subseteq G$ such that the bipartite relation $xy\in A$ omits infinite
half-graphs. Our proofs rely on the characterization of stability via
Grothendieck's "double-limit" theorem (as shown by Ben Yaacov), and the work of
Ellis and Nerurkar on weakly almost periodic $G$-flows.
