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On dilations and contractions in Riesz groups. (English) Zbl 0704.06009

For n,m\(\in N\), a bijection f: \(G\to G\) is called an (m,n)-transposition in a partially ordered group G if \(m| f(x)-f(y)| =n| x- y|\) for each x,y\(\in G\). If \(m<n\) \((m>n)\), then an (m,n)- transposition in an isolated partially ordered group is called a dilation (contraction). The main result establishes the relations between the (m,n)-transpositions in an isolated abelian Riesz group G and the direct decompositions of G. Further, it is shown that (m,n)-transpositions in G preserve certain convex subsets of G.
Reviewer: S.A.Gurchenkov

MSC:

06F15 Ordered groups
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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