## 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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