in this paper we construct the category of coverings of fundamental generalized lie group-groupoid associatedwith a connected generalized lie group. we show that this category is equivalent to the category of coverings of aconnected generalized lie group. in addition, we prove the category of coverings of generalized lie groupgroupoidand the category of actions of this generalized lie group-gro...

Morgenstern ([Mor95]) claimed to have constructed fundamental domains for congruence subgroups of the lattice group Γ = PGL2(Fq[t]), and subgraphs providing the first known examples of linear families of bounded concentrators. His method was to construct the fundamental domain for a congruence subgroup as a ‘ramified covering’ of the fundamental domain for Γ on the Bruhat-Tits tree X = Xq+1 of ...

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...

We develop an algebraic representation for ð1; 1Þ-knots using the mapping class group of the twice punctured torus MCG2ðTÞ. We prove that every ð1; 1Þ-knot in a lens space Lðp; qÞ can be represented by the composition of an element of a certain rank two free subgroup of MCG2ðTÞ with a standard element only depending on the ambient space. As notable examples, we obtain a representation of this t...

Using graph theoretical technique, we present a construction of a (30, 2, 29, 14)-relative difference set fixed by inversion in the smallest finite simple group—the alternating group A5. To our knowledge this is the first example known of relative difference sets in the finite simple groups with a non-trivial forbidden subgroup. A connection is then established between some relative difference ...

A transitive subgroup G ≤ SN is called a genus zero group if there exist non identity elements x1 , . xr∈G satisfying =<x1, xr>, x1·...·xr=1 and ind x1+...+ind xr = 2N − 2. The Hurwitz space Hinr(G) the of coverings Riemann sphere P1 with r branch points monodromy G.In this paper, we assume that finite PSp(4, q) Aut(PSp(4, q)) acts on projective 3-dimensional geometry PG(3, q), q prime po...

The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.

We consider a natural covering responsible for the complexity of the ramification of roots of the general real polynomial equation, and calculate the homology groups of its base; for equations of degree ≤ 5 we give a complete description of the topology of this base. The general complex d-valued entire algebraic function x = F (a1, . . . , ad), given by the equation (1) x + a1x + · · ·+ ad−1x+ ...

The main purpose is to characterise continuous maps that are n-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius n-homomorphisms between two function spaces that correspond to n-branched coverings are determined completely. Several equivalent definitions of a Frobenius n-homomorphism are compared and some of their properties are proved. A...