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For N d-actions by algebraic endomorphisms on compact abelian groups, theexistence of non-mixing configurations is related to "S-unit type" equationsand plays a role in limit theorems for such actions. We consider a family ofendomorphisms on shift-invariant subgroups of F Z d p and show that there arefew solutions of the corresponding equations. This implies the validity of theCentral Limit Theorem for different methods of summation.

Almost mixing of all orders and CLT for some $\mathbb{Z}^d$-actions on subgroups of $\mathbb{F}\_p^{\mathbb{Z}^d}$