On Finite Lattice Coverings

Some combinatorial aspects of finite Hamiltonian groups

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...

ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

Regular Coverings in Filter and Ideal Lattices

The Dedekind–Birkhoff theorem for finite-height modular lattices has previously been generalized to complete modular lattices, using the theory of regular coverings. In this paper, we investigate regular coverings in lattices of filters and lattices of ideals, and the regularization strategy–embedding the lattice into its lattice of filters or lattice of ideals, thereby possibly converting a co...

Finite Groups with p-Sylow Coverings

Tree lattice subgroups

Let X be a locally finite tree and let G = Aut(X). Then G is naturally a locally compact group. A discrete subgroup Γ ≤ G is called an X-lattice, or a tree lattice if Γ has finite covolume in G. The lattice Γ is encoded in a graph of finite groups of finite volume. We describe several methods for constructing a pair of X-lattices (Γ′,Γ) with Γ ≤ Γ′, starting from ‘edgeindexed graphs’ (A′, i′) a...