the textit{commutativity degree}, $pr(g)$, of a finite group $g$ (i.e. the probability that two (randomly chosen) elements of $g$ commute with respect to its operation)) has been studied well by many authors. it is well-known that the best upper bound for $pr(g)$ is $frac{5}{8}$ for a finite non--abelian group $g$. in this paper, we will define the same concept for a finite non--abelian textit{...

A group in which every element commutes with its endomorphic images is called an E-group. If p is a prime number, a p-group G which is an E-group is called a pE-group. Every abelian group is obviously an E-group. We prove that every 2-generator E-group is abelian and that all 3-generator E-groups are nilpotent of class at most 2. It is also proved that every infinite 3-generator E-group is abel...

Recently the construction of the non-abelian effective D-brane action was performed through order α′3 including the terms quadratic in the gauginos. This result can be tested by calculating the spectrum in the presence of constant magnetic background fields and comparing it to the string theoretic predictions. This test was already performed for the purely bosonic terms. In this note we extend ...

1. Thaine’s “purely cyclotomic” method [Th88] for bounding the exponents of the ideal class groups of cyclotomic fields. The bounds that Thaine obtained were already known thanks to the proof of the Main Conjecture by Mazur andWiles, in which unramified abelian extensions of cyclotomic fields were constructed from reducible two-dimensional Galois representations occuring in the Jacobians of mod...

In the context of non-abelian gerbes we define a cubical version of categorical group 2-bundles with connection over a smooth manifold and consider their two-dimensional parallel transport with the aim of defining non-abelian Wilson surface functionals.

A coring approach to non-Abelian descent cohomology of [P. Nuss & M. Wambst, Non-Abelian Hopf cohomology, Preprint arXiv:math.KT/0511712, (2005)] is described and a definition of a Galois cohomology for partial group actions is proposed.

Pairings are particular bilinear maps, and as any bilinear maps they factor through the tensor product as group homomorphisms. Besides, nothing seems to prevent us to construct pairings on other abelian groups than elliptic curves or more general abelian varieties. The point of view adopted in this contribution is based on these two observations. Thus we present an elliptic curve free study of ...

Addison-Wesley has just reissued Serre’s 1968 treatise on l-adic representations in their Advanced Book Classics series. This circumstance presents a welcome excuse for writing about the subject, and for placing Serre’s book in a historical perspective. The theory of l-adic representations is an outgrowth of the study of abelian varieties in positive characteristic, which was initiated by Hasse...

We study static, spherically symmetric, and purely magnetic solutions of SU(2) × SU(2) gauge supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/8 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. These present the first known example of non...

We study the low energy regime of the scattering of two fermionic particles carrying isospin 1/2 and interacting through a non-Abelian Chern-Simons field. We calculate the one-loop scattering amplitude for both the nonrela-tivistic and also for the relativistic theory. In the relativistic case we introduce an intermediate cutoff, separating the regions with low and high loop momenta integration...