We study the periodicity of subshifts of finite type (SFT) on Baumslag-Solitar groups. We show that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs. In particular, this shows that unlike $\mathbb{Z}^2$, but like $\mathbb{Z}^3$, strong and weak aperiodic SFTs are different classes of SFTs in residually finite BS groups. More precisely, we prove that a weakly aperiodic SFT on BS(m,n) due to Aubrun and Kari is, in fact, strongly aperiodic on BS(1,n); and weakly but not strongly aperiodic on any other BS(m,n). In addition, we exhibit an SFT which is weakly but not strongly aperiodic on BS(1,n); and we show that there exists a strongly aperiodic SFT on BS(n,n).

翻译：我们研究了Baumslag-Solitar群上有限型子平移（SFT）的非周期性。我们证明了对于剩余有限Baumslag-Solitar群，既存在强非周期SFT，也存在弱非周期但非强非周期的SFT。特别地，这表明与$\mathbb{Z}^2$不同（但与$\mathbb{Z}^3$类似），在剩余有限的BS群中，强非周期SFT与弱非周期SFT是不同的SFT类别。更精确地说，我们证明了由Aubrun和Kari构造的BS(m,n)上的一个弱非周期SFT，在BS(1,n)上实际上是强非周期的；而在任何其他BS(m,n)上则是弱但非强非周期的。此外，我们构造了一个在BS(1,n)上弱但非强非周期的SFT；并且证明了在BS(n,n)上存在强非周期SFT。