Surface symmetry. II
In this paper the author continues his investigation of orientation preserving actions of a finite group G on a closed oriented connected surface M [part I appeared in ibid. 29, 171-183 (1982; Zbl 0511.57025)]. The groups under consideration are split metacyclic groups, i.e., semidirect products of two cyclic groups. The main results are that free actions of such groups are bijectively classified by \(H_ 2(G;{\mathbb{Z}})\) (Theorem 1.7) and that indecomposable (non-free) actions of G on M are weakly equivalent (i.e. equivalent modulo automorphisms of G) iff they have weakly equivalent fixed point data (Corollary 2.5). The same result also holds for \(G=SL_ 2(F_ q)\) (Corollary 2.9) but it is not true for G the symmetric group \(S_ 5\) as the author constructs two inequivalent, indecomposable actions of \(S_ 5\) on \(M=F_{16}\) (Proposition 2.10).
orientation preserving actions of a finite group
scientific article; zbMATH DE number 3895965