PUB - Publikationen an der Universität Bielefeld

The sets of B-free integers are considered with respect to (reversing) symmetries. It is well known that, for a large class of them, the centraliser of the associated B-free shift (otherwise known as its automorphism group) is trivial. We extend this result to the full centraliser, which effectively shows that all self-homeomorphisms of the B-free shift that commute with some power of the shift are shifts themselves. This also leads to the result that the full normaliser agrees with the normaliser for this class, which is the semidirect product of the centraliser with the cyclic group of order 2 generated by reflection.