Cantor extension of a half linearly cyclically ordered group (Q2773030)

The notion of half linearly cyclically ordered group (half \(\ell c\)-group, for short) was introduced by the reviewer [``On half cyclically ordered groups'', Czechoslovak Math. J. 52, No. 2, 275-294 (2002)] generalizing the notion of half linearly ordered group, which is due to \textit{M. Giraudet} and \textit{F. Lucas} [Fundam. Math. 139, No. 2, 75-89 (1991; Zbl 0766.06014)]. NEWLINENEWLINENEWLINEFrom the author's introduction: Let \(G\) be a half \(\ell c\)-group such that its increasing part is abelian and its decreasing part is nonempty (thus \(G\) fails to be an \(\ell c\)-group). The notions of a convergent sequence and a fundamental sequence are defined in a natural way. If every fundamental sequence in \(G\) is convergent in \(G\), then \(G\) is said to be \(C\)-complete. In the present paper necessary and sufficient conditions are found under which \(G\) is \(C\)-complete. Further, we define the notion of a Cantor extension and we prove that every half \(\ell c\)-group has a Cantor extension which is uniquely determined up to isomorphisms leaving all elements of \(G\) fixed.