Resumen de Some results on O∗-groups

Sebahattin ikikardes, Recep Sahin

• A compact Klein surface with boundary of algebraic genus g ≥ 2 has at most 12(g−1) automorphisms. When a surface attains this bound, it has maximal symmetry, and the group of automorphisms is then called an M∗-group. If a finite group G of odd order acts on a bordered Klein surface X of algebraic genus g ≥ 2, then |G| ≤ 3(g − 1). If G acts with the largest possible order 3(g − 1), then G is called an O∗-group. In this paper, using the results about some normal subgroups of the extended modular group Γ, we obtain some results about O∗-groups. Also, we give the relationships between O∗-groups and M∗-groups.