Automorphism groups of compact planar Klein surfaces
Let \(X=D/\Gamma\) be a 2-sphere with k boundary components, and a Klein surface structure. Let G be a finite group, \(\sigma =(g,\pm,[-],\{(-)^ k\})\) the signature of an NEC-group; \(\sigma'\) the signature of another NEC-group \(\Gamma'\) and \(\theta: \Gamma'\to G\) an epimorphism. The author states some condition on \(\sigma'\) under which the following relations hold: (a) \(G\cong Aut(D/\Gamma)\) and (b) \(G\times {\mathbb{Z}}/(2)\) is an automorphism group of \(D/\ker\theta\). Using these results and the fact that all possible automorphism groups of X are also automorphism groups of the sphere he lists all the automorphism groups of X (theorem 3.1) the proof is based on some technical computational methods.
scientific article; zbMATH DE number 3977158