Group classes and mutually permutable products

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

Products in Residue Classes

Abstract. We consider a problem of P. Erdős, A. M. Odlyzko and A. Sárkőzy about the representation of residue classes modulom by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results “on average” over moduli m and residue classes modulo m and somewhat strong...

Using Cooperative Group Feedback and Cooperative Group Writing in Writing Classes

The present study compared the effect of cooperative group feedback and cooperative group writing techniques in writing classes. Accordingly, 90 male and female intermediate English language learners sat for a sample piloted Preliminary English Test and 60 who scored one standard deviation above and below the mean were selected as the main participants. Both groups were taught the same course b...

Group Testing with Multiple Mutually-Obscuring Positives

Group testing is a frequently used tool to identify an unknown set of defective (positive) elements out of a large collection of elements by testing subsets (pools) for the presence of defectives. Various models have been studied in the literature. The most studied case concerns only two types (defective and non-defective) of elements in the given collection. This paper studies a novel and natu...

Partitioning networks into classes of mutually isolated nodes ?

Following the work of Newman, we model complex networks with random graphs of a given degree distribution. In particular we study the case where all vertices have exactly the same degree (random regular graphs). We survey some recent results on the problem of partitioning such a graph into the smallest possible number of classes of mutually isolated vertices, known in graph theory as the colora...