  In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras
of conjugacy classes of symmetric groups $S_n$ admit a stabilization (in a
non-obvious sense) as $n\to \infty$. We extend their construction to a class of
pairs of groups $G\supset K$ and algebras of conjugacy classes of $G$ with
respect to $K$. In our basic example $G$ is a product of symmetric groups,
$G=S_n \times S_n$, $K$ is the diagonal subgroup $S_n$.
