Normal coverings of linear groups

Normal coverings of finite symmetric and alternating groups

In this paper we investigate the minimum number of maximal subgroups Hi, i = 1 . . . k of the symmetric group Sn (or the alternating group An) such that each element in the group Sn (respectively An) lies in some conjugate of one of the Hi. We prove that this number lies between aφ(n) and bn for certain constants a, b, where φ(n) is the Euler phi-function, and we show that the number depends on...

On subgroups of topologized fundamental groups and generalized coverings

‎In this paper‎, ‎we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps‎. ‎More precisely‎, ‎we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology‎. ‎Moreover‎, ‎we present some conditions unde...

Finite Groups with p-Sylow Coverings

Veech Groups and Polygonal Coverings

We discuss branch points of a ne coverings and their e ects on Veech groups. In particular, this allows us to show that even if one polygon tiles another, the respective Veech groups are not necessarily commensurable. We also show that there is no universal bound on the number of Teichm uller disks passing through the same point of Teichm uller space and having incommensurable lattice Veech g...

Monodromy Groups of Coverings of Curves

We consider nite separable coverings of curves f : X → Y over a eld of characteristic p ≥ 0. We are interested in describing the possible monodromy groups of this cover if the genus of X is xed. There has been much progress on this problem over the past decade in characteristic zero. Recently Frohardt and Magaard completed the nal step in resolving the Guralnick Thompson conjecture showing that...