A Hurwitz group is a finite group of orientation-preserving diffeomorphisms of maximal possible order 84(g − 1) of a closed orientable surface of genus g > 1. A maximal handlebody group instead is a group of orientation-preserving diffeomorphisms of maximal possible order 12(g − 1) of a 3-dimensional handlebody of genus g > 1. We consider the question of when a Hurwitz group acting on a surface of genus g contains a subgroup of maximal possible order 12(g − 1) extending to a handlebody (or… Expand

We show that every action of a finite dihedral group on a closed orientable surface F extends to a 3-dimensional handlebody V , with ∂V = F . In the case of a finite abelian group G, we give… Expand

Let G be a finite group of orientation preserving isometrics of a closed orientable hyperbolic 2-manifold F g of genus g > 1 (or equivalently, a finite group of conformal automorphisms of a closed… Expand

Abstract Every finite group of symmetries (homeomorphisms) of a compact bounded surface of algebraic genus g acts, by taking the product with the interval [0,1], also on the 3-dimensional handlebody… Expand

The problem of classifying all finite group actions, up to topological equivalence, on a surface of low genus is considered. Several new examples of construction and classification of actions are… Expand