Given a finite group G, we consider the problem of finding the maximal size nc(G) of subsets of G that have the property that no two of their elements of commute. After constructing a large noncommuting subset of Sn, we consider the definition and classification of extraspecial p-groups and focus on such a group: S(p.n). We show that nc(S(2, n)) = 2n+ 1 and that S(p, n) ≥ pn+ 1.

We give the maximal distance between a copula and itself when the argument is permuted for arbitrary dimension, generalizing a result for dimension two by Nelsen (2007); Klement and Mesiar (2006). Furthermore, we establish a subset of [0, 1] in which this bound might be attained. For each point in this subset we present a copula and a permutation, for which the distance in this point is maximal...

In this paper, we investigate the non-interactive simulation proposed by Kamath et. al. [3], and establish outer bounds by using the maximal correlation and hypercontractivity ribbon. For several examples, inner bounds are discussed and explicit schemes are also introduced.

Given a set P n of n points on the plane labeled with the integers f1; : : : ; ng, an increasing path of P n is a sequence of points i 1 < : : : < i k such that the polygonal path ob-1 is non-self intersecting. We show that any point set on the plane admits an increasing path of length at least p 2n. We also study the problem of nding the longest common increasing path of two convex point sets ...

I review recent progress in the construction and classification of maximally supersymmetric theories with non-abelian gauge groups. The algebraic framework is based on the underlying exceptional symmetry groups. This has applications for supergravity theories describing flux compactifications as well as for the recently constructed three-dimensional superconformal theories describing the dynami...

we discuss whether finiteness properties of a profinite group $g$ can be deduced from the coefficients of the probabilisticzeta function $p_g(s)$. in particular we prove that if $p_g(s)$ is rational and all but finitely many non abelian composition factors of $g$ are isomorphic to $psl(2,p)$ for some prime $p$, then $g$ contains only finitely many maximal subgroups.

let $g$ be a non-abelian group of order $p^n$‎, ‎where $nleq 5$ in which $g$ is not extra special of order $p^5$‎. ‎in this paper we determine the maximal size of subsets $x$ of $g$‎ ‎with the property that $xyneq yx$ for any $x,y$ in $x$ with‎ ‎$xneq y$‎.

In traditional system of Indian medicine, C.bonducella is widely used for its antipyretic, antiperiodic, anticonvulsive, and antiparalytic activities. For assessing anticonvulsant activity, pentylenetetrazole, maximal electro shock, strychnine- and picrotoxin-induced convulsions models were used. Diazepam was used as a standard reference for all models except maximal electro shock model, wh...