Parabolically connected subgroups

Connected transversals to subnormal subgroups

Subnormal subgroups possessing connected transversals are briefly discussed.

Beam propagation in parabolically tapered graded-index waveguides.

To a good approximation, the electromagnetic-propagation characteristics of graded-index waveguides can be written in terms of polynomial-Gaussian modes. For uniform quadratic-index waveguides the behavior of these modes is well known. However, there are sometimes practical reasons for using tapered waveguides, but detailed propagation solutions are known for only a few specific taper functions...

Multifractal Analysis for Parabolically Semihyperbolic Generalized Polynomial-like Maps

On Connected Transversals to Subgroups Whose Order is a Product of Two Primes

We consider finite groups which have connected transversals to subgroups whose order is a product of two primes p and q. We investigate those values of p and q for which the group is soluble. We can show that the solubility of the group follows if q = 2 and p ≤ 61, q = 3 and p ≤ 31, q = 5 and p ≤ 11. We then apply our results on loop theory and we show that if the inner mapping group of a finit...

Institute for Mathematical Physics Connected Subgroups of So(2,n) Acting Irreducibly on R 2,n

We classify all connected subgroups of SO(2, n) that act irreducibly on R. Apart from SO0(2, n) itself these are U(1, n/2), SU(1, n/2), if n even, S 1·SO(1, n/2) if n even and n ≥ 2, and SO0(1, 2) for n = 3. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex hyperbolic space and of the Lie ball. As an application we obtain a lis...