E-Prints Complutense

Abstract

A Klein surface X is a surface with a dianalytic structure. If its topological genus is g and it has k boundary components then its algebraic genus is p=2g+k−1 (X orientable) and p=g+k−1 (X nonorientable). A Klein surface of algebraic genus p has at most 12(p−1) automorphisms and if this bound is attained then AutX is called an M ∗ -group. In this paper the author finds families of M ∗ -groups and determines the topological type of the surface on which they act. The groups he deals with are those of the form G m,n,q considered by H. M. S. Coxeter [Trans. Amer. Math. Soc. 45 (1939), 73--150; Zbl 20, 207]: PSL(2,q), q≡1mod4, PGL(2,q), q≡3mod4 and PSL(2,2 m ) . For related work see a paper by N. Greenleaf and C. L. May [ibid. 274 (1982), no. 1, 265--283]