Abstract

We generalize a result of Hochman in two simultaneous directions: instead of realizing an arbitrary effectively closed Z(d) action as a factor of a subaction of a Z(d+2)-SFT we realize an action of a finitely generated group analogously in any semidirect product of the group with Z(2). Let H be a finitely generated group and G = Z(2) x(phi) H a semidirect product. We show that for any effectively closed H-dynamical system (Y, T) where Y subset of {0, 1}(N), there exists a G-subshift of finite type (X, sigma) such that the H-subaction of (X, sigma) is an extension of (Y, T). In the case where T is an expansive action, a subshift conjugated to (Y, T) can be obtained as the H-projective subdynamics of a sofic G-subshift. As a corollary, we obtain that G admits a non-empty strongly aperiodic subshift of finite type whenever the word problem of H is decidable.