ON SOLUBLE GROUPS OF AUTOMORPHISMS OF NONORIENTABLE KLEIN SURFACES

We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q greater-than-or-equal-to 2 has at most 24(q - 1) elements and that this bound is sharp for infinitely many values of q.