Direct topological factorization for topological flows

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This paper considers the general question of when a topological action of a countable group can be factored into a direct product of a nontrivial actions. In the early 1980's D. Lind considered such questions for Z-shifts of finite type. We study in particular direct factorizations of subshifts of finite type over Zᵈ and other groups, and Z-subshifts which are not of finite type. The main results concern direct factors of the multidimensional full n-shift, the multidimensional 3-colored chessboard and the Dyck shift over a prime alphabet. A direct factorization of an expansive G-action must be finite, but a example is provided of a non-expansive Z-action for which there is no finite direct prime factorization. The question about existence of direct prime factorization of expansive actions remains open, even for G=Z.