Circular totally semi-ordered groups. (English) Zbl 0849.06014

The author investigates circular totally semi-ordered groups for the cases having strictly positive elements. Main results: Let \(G\) be a circular totally semi-ordered group with the least strictly positive element \(a\). Then there is no element \(x\) in \(G\) such that \(0 < x\), \(-x < x\) and \(x < (-n)a\) for some \(n \in \mathbb{N}\). Moreover, if \(a\) has infinite order, then the subgroup \([a]\) generated by \(a\) in \(G\) is the least of all proper subgroups \(H\) of \(G\) such that \(H^+\) is convex in \(G^+\).
Reviewer: B.F.Šmarda (Brno)


06F15 Ordered groups


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