  We obtain the following embedding theorem for symbolic dynamical systems. Let
$G$ be a countable amenable group with the comparison property. Let $X$ be a
strongly aperiodic subshift over $G$. Let $Y$ be a strongly irreducible shift
of finite type over $G$ which has no global period, meaning that the shift
action is faithful on $Y$. If the topological entropy of $X$ is strictly less
than that of $Y$, and $Y$ contains at least one factor of $X$, then $X$ embeds
into $Y$. This result partially extends the classical result of Krieger when $G
= \mathbb{Z}$ and the results of Lightwood when $G = \mathbb{Z}^d$ for $d \geq
2$. The proof relies on recent developments in the theory of tilings and
quasi-tilings of amenable groups.
