Products and decompositions of adding machines

In this paper we give several necessary and sufficient conditions for the product fK of a countable family of adding machines to be topologically conjugate to an adding machine fK. We also study decompositions of adding machines fK, of carry systems K and of K-adic topological groups ΣK, investigate the relation between these decompositions, and obtain some necessary and sufficient conditions for a K-adic topological group ΣK to be decomposable to the direct product of a family of its compact subgroups. In addition, equivalent conditions of an adding machine having a non-trivial periodic orbit factor are given, and the calculation of elements of finite orders in K-adic topological groups ΣK is discussed.