  Let $G$ be an infinite countable discrete amenable group. For any $G$-action
on a compact metric space $X$, it is proved that for any sequence $(G_n)_{n\ge
1}$ consisting of non-empty finite subsets of $G$ with $\lim_{n\to
\infty}|G_n|=\infty$, Pinsker $\sigma$-algebra is a characteristic factor for
$(G_n)_{n\ge 1}$. As a consequence, for a class of $G$-topological dynamical
systems, positive topological entropy implies mean Li-Yorke chaos along a class
of sequences consisting of non-empty finite subsets of $G$.
