Generalized \(M^*\)-simple groups (Q350778)

Let \(G\) be a group of automorphisms of a compact bordered Klein surface \(X\) of algebraic genus \(p > 1\). By work of \textit{C. L. May} [Glasg. Math. J. 18, 1--10 (1977; Zbl 0363.14008)], it is known that \(|G| \leq 12(p-1)\). When the upper bound is attained, the automorphism group \(G\) of \(X\) acts with signature \(\big(0; +; [-]; \{(2,2,2,3)\}\big)\), and is called an \(M^*\)-group.NEWLINENEWLINEIn this paper the authors make some basic observations about actions of groups with signature \(\big(0; +; [-]; \{(2,2,2,q)\}\big)\) for any odd prime \(q\). In any such case, \(|G| = {4q \over q-2}(p-1)\), and \(G\) is an example of what they call a generalized \(M^*\)-group. They also say \(G\) is generalized \(M^*\)-simple if it has no proper quotient that is a generalized \(M^*\)-group.