Generalized M*-groups

Abstract

A compact bordered Klein surface of algebraic genus p >= 2 has at most 12(p - 1) automorphisms. Automorphism groups which attain this bound are called M*-groups. In this paper, firstly, we define generalized M*-groups. Then, we show that there is a relationship between the extended Hecke groups and generalized M*-groups. Finally, we prove that a generalized M*-group G is supersoluble if and only if vertical bar G vertical bar = 4 (.) q(r) for q >= 3 prime number and for some positive integer r.