Finite abelian surface coverings

Finite Groups with p-Sylow Coverings

Coverings of Abelian groups and vector spaces

We study the question how many subgroups, cosets or subspaces are needed to cover a finite Abelian group or a vector space if we have some natural restrictions on the structure of the covering system. For example we determine, how many cosets we need, if we want to cover all but one element of an Abelian group. This result is a group theoretical extension of the theorem of Brouwer, Jamison and ...

On Finite Lattice Coverings

We consider nite lattice coverings of strictly convex bodies K. For planar centrally symmetric K we characterize the nite arrangements Cn such that conv Cn Cn + K, where Cn is a subset of a covering lattice for K (which satisses some natural conditions). We prove that for a xed lattice the optimal arrangement (measured with the parametric density) is either a sausage, a socalled double sausage ...

Abelian coverings of finite general linear groups and an application to their non-commuting graphs

In this paper we introduce and study a family An(q) of abelian subgroups of GLn(q) covering every element of GLn(q). We show that An(q) contains all the centralizers of cyclic matrices and equality holds if q > n. For q > 2, we obtain an infinite product expression for a probabilistic generating function for |An(q)|. This leads to upper and lower bounds which show in particular that c1q −n ≤ |A...

Finite Coverings and Rational Points

The purpose of this talk is to put forward a conjecture. The background is given by the following Basic Question. Given a (smooth projective) curve C over a number field k, can we determine explicitly the set C(k) of rational points? One possible approach to this is to consider an unramified covering D π → C that is geometrically Galois. By standard theory, there are only finitely many twists D...