The finite subgroups of \(\mathrm{PGL}_2({\mathbb {C}})\) are shown to be the only groups G with this property: for some integer \(r_0\) (depending on G), all Galois covers \(X\rightarrow {\mathbb {P}}^1_{\mathbb {C}}\) group can obtained by pulling back those at most branch points along non-constant rational maps \({\mathbb {C}}\rightarrow {C}}\). For \(G\subset \mathrm{PGL}_2({\mathbb {C}})\)...

Motivated by quotient algorithms, such as the well-known $p$-quotient or solvable we describe how to compute extensions $\tilde H$ of a finite group $H$ direct sum isomorphic simple $\mathbb{Z}_p H$-modules that and have same number generators. Similar other our description will be via suitable covering $H$. Defining this requires study representation module, introduced Gasch\"utz in 1954. Our ...

For a random walk on finitely generated group G we obtain generalization of classical inequality Ancona. We deduce as corollary that the identity map extends to continuous equivariant surjection from Martin boundary Floyd boundary, with preimages conical points being singletons. This provides new results for compactifications relatively hyperbolic groups.

An orthogonal cover of the complete digraph ~ K n is a collection of n spanning subgraphs ~ K n such that-every directed edge of ~ K n belongs to exactly 1 of the ~ G i 's and-for every two digraphs ~ G i and ~ G j (i 6 = j) there is a unique two-element set fa; bg of vertices such that ~ G i contains the directed edge (a; b) and ~ G j contains the directed edge (b; a). It is proven that there ...

Lovász and Stein (independently) proved that any hypergraph satisfies τ ≤ (1+ln ∆)τ * , where τ is the transversal number, τ * is its fractional version, and ∆ denotes the maximum degree. We prove τ f ≤ 3.17τ * max{ln ∆, f } for the f-fold transversal number τ f. Similarly to Lovász and Stein, we also show that this bound can be achieved non-probabilistically, using a greedy algorithm. As a com...

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...