On Oikawa's theorem from an algebraic and geometric point of view. (Q1423851)

The authors give a new proof of the following theorem: Given a bordered compact Klein surface \(X\) with \(k\) boundary components and a group of automorphisms \(G\) there exists an unbordered compact Klein surface \(\widetilde X\) of the same topological genus and orientability character for which \(G\) is a group of automorphisms. This was first proved for Riemann surfaces, in 1956, by \textit{K. Oikawa} [in Kodai Math. Semin. Rep. 8, 23-30 (1956; Zbl 0072.07702)]. As an application they give some considerations about relations between fundamental regions of related NEC groups.