Notes on Brown-McCoy-radicals for Γ-near-rings

The Brown-McCoy radical is known to be an ideal-hereditary Kurosh-Amitsur radical in the variety of zerosymmetric near-rings. We define the Brown-McCoy and simplical radicals, and , respectively, for zerosymmetric -near-rings. Both and are ideal-hereditary Kurosh-Amitsur radicals in that variety. IfM is a zerosymmetric -near-ring with left operator near-ringL, it is shown that , with equality ifM has a strong left unity. is extended to the variety of arbitrary near-rings, and and are extended to the variety of arbitrary -near-rings, in a way that they remain Kurosh-Amitsur radicals. IfN is a near-ring andA N, then , with equality ifA if left invariant.     

A Helly-type theorem for simple polygons

Let be a family of simple polygons in the plane. If every three (not necessarily distinct) members of have a simply connected union and every two members of have a nonempty intersection, then {P:P in } . Applying the result to a finite family of orthogonally convex polygons, the set {C:C in } will be another orthogonally convex polygon, and, in certain circumstances, the dimension of this intersection can be determined.Supported in part by NSF grant DMS-9207019.     

Universality of the automorphism group of the real line

We discuss the question, whether each automorphism group (of cardinality at most ) of a linear order is embeddable into the automorphism group of the real line. We show that the answer to this question is independent of the axioms of ZFC: the answer is positive, if we assume < and Souslin's hypothesis; the answer is negative, if we assume orV=L.     

Sylow subgroups of finitary linear groups

In this paper we describe the structure and the conjugacy classes of Sylow p-subgroups of FGL(V, ), the group of finitary -automorphisms of the -vector space V.The Author is member of the GNSAGA.     

On causality in commutant lifting theorem. I

Two functionals (A) and for an operatorA were introduced in [11] for the study of causality in commutant lifting theory. In this paper we give sufficient and necessary conditions for in a special case. We prove that in this case , and we show by some examples related to nonlinear system control that is the best constant in our inequality.     

Operator inequalities and construction of Krein spaces

Let be a Hilbert space. A continuous positive operatorT on uniquely determines a Hilbert space which is continuously imbedded in and for which with the canonical imbedding . A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space ( ) which is continuously imbedded in and for which with the canonical imbedding .     

Small complete arcs in andré planes of square order

A complete arc in a projective plane of orderq has at least points. We show the existence of completek-arcs having points in certain André planes of square order. Moreover our construction shows that for all x > \sqrt q \log q$$ " align="middle" border="0"> there are completek-arcs withx < k < Cxlogq, for some absolute constantC.     

K-theory of twisted differential operators on flag varieties

Let be a semisimple Lie algebra overk, an algebraically closed field of characteristic zero, and let be a Cartan subalgebra inside a Borel subalgebra of . LetU be the enveloping algebra of . For letM() denote the corresponding Verma modúle and letU _u=U/AnnM(). LetW be the Weyl group and letW ⁰ be the stabiliser of inW. We prove the following theorem, which affirms a conjecture of T.J. Hodges.Oblatum 16-XII-1994     

Operators of fibered groups

Let (G, ) denote a finite groupG with fibration . The group Aut (G, ) of operators of (G, ) is closely related to the group of collineations of (G, ). In this paper we investigate the geometric properties imposed on (G, ) by requiring that Aut (G, )=AutG. We find that in many instances this algebraic property restricts the geometry to a very special form.Dedicated to Professor Helmut Karzel on the occasion of his 60th birthday.     

Quotient Groups of Groups of Certain Classes

For an arbitrary variety of groups and an arbitrary class of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with - and -factors (respectively, is a residually -group) if G possesses an invariant system with - and -factors (respectively, is a residually -group) and N (respectively, N is a maximal invariant -subgroup of the group G).