. 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

Let Vg be an orientable three-dimensional handlebody with genus g > 1. Let N(g) be the largest order among all finite groups which act effectively on Vg and preserve orientation. We show that 4(g +… Expand

In [4] the authors observed that the topological methods in the theory of three-dimensional manifolds can be modified to settle some old problems in the classical theory of minimal surfaces in… Expand