In this note it will be shown that when A is a retract (cf. [3])1 of X, then the same relationship holds between the universal covering spaces of A and X (Theorem 1.1) and also between the fundamental groups of A and X (Theorem 2.2). We denote the universal covering space of X by X*, where pEX, and the fundamental group by iriX) [l]. All spaces are assumed to be arcwise connected, Hausdorff spa...

The graphs considered in this paper are finite, undirected and simple. For a graph G, we denote its vertex set by V (G) and its edge set by E(G). A graph labeling, as introduced in [8], is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Over the years, a large variety of different types of graph labelings have been studied, see [2] for an extensive su...

A topological space is called paracompact (see [2 J) if (i) it is a Hausdorff space (satisfying the T2 axiom of [l]), and (ii) every open covering of it can be refined by one which is "locally finite" ( = neighbourhood-finite; that is, every point of the space has a neighbourhood meeting only a finite number of sets of the refining covering). J. Dieudonné has proved [2, Theorem 4] that every se...

We study pairs (G,A) where G is a finite group and A < G is maximal, satisfying ⋃ g∈G (Ax) = G − {1G} for all x ∈ G − A. We prove that this condition defines a class of permutation groups, denoted CCI, which is a subclass of the class of primitive permutation groups. We prove that CCI contains the class of 2-transitive groups. We also prove that groups in CCI are either affi ne or almost simple...

In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck’s discrete transformation group) of a digital covering. By using these to...

Porcine small intestinal submucosa (SIS) was shown to be an effective bioscaffold in enhancing the mechanical properties of healing medial collateral ligaments (MCL). The purpose of this study was to investigate whether there are corresponding improvements in morphology and tissue compositions. Fourteen rabbits were equally divided into two groups. In the SIS-treated group, a 6 mm gap was surgi...

every seifert fibre group is the lift of a fuchsian group to the universal covering group of psl (2,r). from this, we work out a form of presentation for such a group. with the calculation of the euler number, we can establish the presentation of the derived group of a seifert fibre group

The quantity g (k) (v) was introduced in [6] as the minimum number of blocks necessary in a pairwise balanced design on v elements, subject to the condition that the longest block has length k. Recently, we have needed to use all possibilities for such minimal covering designs, and we record all non-isomorphic solutions to the problem for v ≤ 13.

A covering array CA(N ; t, k, v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. One application of these objects is to generate software test suites to cover all t-sets of component interactions. Methods for construction of covering arrays for software testing have focused on two main areas. The first i...

We prove the homotopy invariance of L torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the L cohomology of the covering space vanishes, the homotopy invariance was established by Lück [Lu]. We also give some applications of our results.