Abstract

It is known that the maximal order of a cyclic group of automorphisms admitted by a Klein surface or real algebraic curve of algebraic genus p is 2p or 2(p + 1), depending on whether p is odd or even. In this paper, we classify the automorphism groups of all non-orientable Klein surfaces, without boundary, which admit an automorphism group of order 2p, or 2(p + 1). We determine that the automorphism groups are cyclic precisely when the surfaces are hyperelliptic. Defining equations for all but one family of these Klein surfaces are given.

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