THE RELATION BETWEEN ADDING MACHINE AND p−ADIC INTEGERS
THE RELATION BETWEEN ADDING MACHINE AND p−ADIC INTEGERS
In this paper, we equip Aut(X) with a natural metric and givean elementary proof that the closure of the adding machine group, a subgroupof the automorphism group, is both isometric and isomorphic to the group ofp−adic integers. This also shows that the group of p−adic integers can beisometrically embedded into the metric space Aut(X∗)
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