Reactions of organic halides with a trigonal pyramidal nickel(0) complex

The nickel(0) comlex [Ni(np₃)], np₃  tris(2-diphenylphinoethyl)amine, which has a trigonal pyramidal geometry in the solid state, readily reacts in solution with organic halides (CH₃I, C₂H₅Cl, C₃H₇Cl, C₆H₅Cl, C₆H₅Br, C₆H₅I and C₆H₅CH₂Cl) to give nickel(I) species with formula [NiX(np3)], (X  Cl, Br, I). Benezene, biphenyl, o-, m-, p-chlorobiphenyl are the other products from the reaction between the title complex and chlorobenzene.     

On the automorphism group of inversive planes of odd order

The structure of the fix bundle free automorphism groups of inversive planes of odd order is determined. As a special case of our main result, the automorphism groups with a transitive action on the points of an inversive plane of odd order are essentially determined, and the plane is shown to be miquelian when these have no non-trivial normal subgroups of odd order.     

The structure of a collineation group preserving an oval in a projective plane of odd order

We investigate the structure of a collineation groupG preserving an oval in a finite projective plane of odd order and we obtain several results aboutG, whenG is a2-group. These results are then used to investigate the structure ofG/O(G) in the general case and, in particular, that ofF*(G/O(G)).This research was supported in part by a grant from the M.U.R.S.T.     

Translation planes of order q 2 admitting a two-transitive orbit of length q + 1 on the line at infinity

A classification is given of all translation planes of order q ² that admit a collineation group G admitting a two-transitive orbit of q + 1 points on the line at infinity.     

Invariant convex sets in polar representations

We study a compact invariant convex set E in a polar representation of a compact Lie group. Polar representations are given by the adjoint action of K on p, where K is a maximal compact subgroup of a real semisimple Lie group G with Lie algebra g = k ⊕ p. If a ? p is a maximal abelian subalgebra, then P = E ∩ a is a convex set in a. We prove that up to conjugacy the face structure of E is completely determined by that of P and that a face of E is exposed if and only if the corresponding face of P is exposed. We apply these results to the convex hull of the image of a restricted1 momentum map.     

Two-transitive parabolic ovals

We investigate finite affine planes of even order possessing a parabolic oval and a collineation group G which leaves invariant and acts 2-transitively on its affine points. The main attention is devoted to translation planes. The odd order case has already been considered by Enea and Korchmaros in [5]. Our main result shows that if has even order and possesses two 2-transitive parabolic ovals which share at least two, but not all their affine points, then is Desarguesian. Received 20 July 1998.     

Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spaces

We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with constant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously, and in the case of finitely generated Abelian groups the necessary and sufficient conditions are given.