Automorphisms of Toeplitz $\mathscr {B}$-free systems

For each $\mathscr {B}$-free subshift given by $\mathscr {B}=\{2^ib_i\}_{i\in {\mathbb {N}}}$, where $\{b_i\}_{i\in {\mathbb {N}}}$ is a set of pairwise coprime odd numbers greater than one, it is shown that the automorphism group of the subshift consists solely of powers of the shift.