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