Aut(T_{n,r}) is exactly the bi-synchronizing transducer subgroup T B_{n,r} that preserves the cyclic order, and Out(T_{n,r}) contains a copy of Thompson's group F for n ≥ 3.
Automorphisms of generalized Thompson groups
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Automorphisms of the generalised Thompson's group $T_{n,r}$
Aut(T_{n,r}) is exactly the bi-synchronizing transducer subgroup T B_{n,r} that preserves the cyclic order, and Out(T_{n,r}) contains a copy of Thompson's group F for n ≥ 3.