in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...

In this paper we study when a bipartite graph is a covering of a non-bipartite graph. We give a characterization of all coverings in terms of factoring the covering map through the canonical double covering. We also consider regular bipartite coverings described in terms of voltage assignments. We give an algebraic characterization of such coverings involving the subgroup generated by voltages ...

Let G be a complex reductive group. A normal G-variety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form local models for multiplicity free Hamiltonian Kmanifolds, K a maximal compact subgroup of G. In this paper, we classify all smooth affine spherical varieties up to coverings, cent...

We show that if a group G acting faithfully on a rooted tree T has a free subgroup, then either there exists a point w of the boundary @T and a free subgroup of G with trivial stabilizer ofw, or there existsw 2 @T and a free subgroup ofG fixingw and acting faithfully on arbitrarily small neighborhoods of w. This can be used to prove the absence of free subgroups for different known classes of g...

A subgroup H of a group G is conjugately dense in G if for each element g in G the intersection of H with the conjugates of g in G is nonempty. Conjugately dense subgroups deal with interesting open problems, related to parabolic groups. In the present paper we study them with respect to suitable coverings. 2000 Mathematics Subject Classification: 20E45, 20B35, 20F99.

Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of applications, ranging from counting branched coverings of Riemann surfaces, to subgroup growth an...