quasinormal subgroups have been studied for nearly 80 years. in finite groups, questions concerning them invariably reduce to p-groups, and here they have the added interest of being invariant under projectivities, unlike normal subgroups. however, it has been shown recently that certain groups, constructed by berger and gross in 1982, of an important universal nature with regard to the existen...

We introduce and study the notions of a strongly completable and of a strongly complete quasi-uniform space. A quasi-uniform space (X,U) is said to be strongly complete if every Cauchy filter (in the sense of Sieber and Pervin) clusters in the uniform space (X,U ∨ U−1). An interesting motivation for the study of this notion of completeness is the fact, proved here, that the quasi-uniformity ind...

We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a ...

In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant sub-spaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.

The aim of this work is to extend the study of super-coinvariant polynomials, introduced in [2, 3], to the case of the generalized symmetric group Gn,m, defined as the wreath product Cm ≀ Sn of the symmetric group by the cyclic group. We define a quasi-symmetrizing action of Gn,m on Q[x1, . . . , xn], analogous to those defined in [12] in the case of Sn. The polynomials invariant under this act...

We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2, a Cantor set of Lyapounov orbits survives the perturbation. The orbits are perturbed to quasi-periodic invariant tori. We show that for a certain family of m...

We consider a minimal equicontinuous action of finitely generated group $ G on Cantor set X with invariant probability measure \mu $, and the stabilizers points for such an action. give sufficient conditions under which there exists subgroup H that in whose are conjugate to has full measure. The is locally quasi-analytic non-degenerate. An if its elements have unique extensions subsets uniform ...