Real genus 12
Let \(G\) be a finite group. The real genus of \(G\) is the minimum algebraic genus of any compact bordered Klein surface on which \(G\) acts as a group of automorphisms. \textit{C. L. May} has proved that for infinitely many integers \(p>2\) there exist groups of the real genus \(p\) but no group of the real genus 2 [Rocky Mt. J. Math. 23, No. 2, 707--724 (1993; Zbl 0795.30039)]. Then we have a question whether there is \(p>2\) such that there exists no group of the real genus \(p\). In this paper the author shows that there exists no group of the real genus 12. A group \(G\) is represented by a factor group \(\Lambda/\Gamma\) of two NEC groups \(\Lambda\) and \(\Gamma\), where \(\Gamma\) is a bordered surface group normalizing a Klein surface. Considering the signatures of \(\Lambda\) and the presentations of \(G\), the author gets the result.
scientific article; zbMATH DE number 2143234
scientific article