Decoding in the automorphism group of a recursively saturated model of arithmetic

The main result of this paper partially answers a question raised in about the existence of countable just recursively saturated models of Peano Arithmetic with non-isomorphic automorphism groups. We show the existence of infinitely many countable just recursively saturated models of Peano Arithmetic such that their automorphism groups are not topologically isomorphic. We also discuss maximal open subgroups of the automorphism group of a countable arithmetically saturated model of PA in a very good interstice.