Cyclic groups of automorphisms of compact non-orientable Klein surfaces without boundary (Q797723)

Referring to previous work [e.g. \textit{W. J. Harvey}, Q. J. Math., Oxf. II. Ser. 17, 86-97 (1966; Zbl 0156.089)] on closed Riemann surfaces as the corresponding case for compact orientable Klein surfaces without boundary, the author considers the problem of finding the minimum genus of surfaces for which a given finite group G is a group of automorphisms. As a preliminary to the study of the general problem, he obtains the minimum genus for the compact non-orientable Klein surfaces having a given cyclic group of automorphisms. As a sample result we may quote: The minimum genus of a non-orientable Klein surface with group of automorphisms isomorphic to \({\mathbb{Z}}_ n\) is n/2 (resp. \(n/2+1)\) if the highest power of 2 which divides n is 1 (resp. \(>1)\). - For odd n the formulae are a little more complicated.