THE RELATION BETWEEN ADDING MACHINE AND p−ADIC INTEGERS

Year 2013, Volume: 1 Issue: 2, 41 - 49, 01.12.2013

Mustafa Saltan

Abstract

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∗)

Keywords

p−adic integers, Adding machine, Automorphism group, p−ary rootedtree

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