Singerman, David; Watson, Paul Non-maximal cyclic group actions on compact Riemann surfaces. (English) Zbl 0903.20027 Rev. Mat. Univ. Complutense Madr. 10, No. 2, 423-439 (1997). A finite group \(G\) of automorphisms of a Riemann surface \(X\) is non-maximal in genus \(g\) if (i) \(G\) acts as a group of automorphisms of some compact Riemann surface \(X_g\) of genus \(g\) and (ii), for all such surfaces \(X_g\), \(|\operatorname{Aut} X_g|>| G|\). The authors investigate the case where \(G\) is a cyclic group \(C_n\) of order \(n\). Then they obtain that if \(C_n\) acts on only finitely many surfaces of genus \(g\), then they completely solve the problem of finding all such pairs \((n,g)\). Also they find a bound for \(n\) as function of genus \(g\) if \(C_n\) acts on infinitely many surfaces of genus \(g\). Reviewer: E.Bujalance (Madrid) Cited in 2 Documents MSC: 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) 30F10 Compact Riemann surfaces and uniformization 20F29 Representations of groups as automorphism groups of algebraic systems Keywords:groups of automorphisms; compact Riemann surfaces; cyclic groups PDFBibTeX XMLCite \textit{D. Singerman} and \textit{P. Watson}, Rev. Mat. Univ. Complutense Madr. 10, No. 2, 423--439 (1997; Zbl 0903.20027) Full Text: EuDML