Maximal arcs in Desarguesian planes of odd order do not exist

Forq an odd prime power, and 1<n<q, the Desarguesian planePG(2,q) does not contain an(nq–q+n,n)-arc.Supported by Italian M.U.R.S.T. (Research Group onStrutture geometriche, combinatoria, loro applicazioni) and G.N.S.A.G.A. of C.N.R.     

Finite groups and subgroup-permutability

Subgrouppermutability in a finite group is studied, in order to distinguish between irreducible and reducible groups and to give a bound for the diameter. A simple nonabelian finite group is irreducible and its diameter is less or equal16 while a reducible group is forced to be soluble and the bound of the diameter of such a group is 4.Research partially supported by G.N.S.A.G.A. of C.N.R. and M.U.R.S.T. of Italy.     

Complete unital-derived arcs in the hall planes

We prove the existence of complete (q ² -q + 1)-arcs in each Hall plane of orderq ²,q ² > 9. Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council) of Italy and supported by M.U.R.S.T. progetto “Strutture Geometriche Combinatoria e Loro Applicazioni”.     

Derived semifield planes with affine elations

Derived semifield planes admitting non trivial affine elations with more than one centre are examined in detail and several new examples of such plantes are constructed. A new characterization of the Hall planes of even order among derived semifield planes is also given.Research partially supported by G.N.S.A.G.A. (C.N.R.)     

Arcs in Minkowski planes

The aim of this paper is to study some properties of k-arcs in Minkowski planes focalizing the attention on problems of existence and completness.Work done under the auspicies of G.N.S.A.G.A. supported by 40% grants of M.U.R.S.T.In memoriam Giuseppe Tallini     

Derived semifield planes of odd order admitting a dihedral group of affine homologies

Derived semifield planes of odd order admitting non-trivial involutorial affine homologies with more than one axis, are examined in detail, under the assumption that the group generated in the translation complement is dihedral. The whole structure of the semifields S coordinatizing such planes is determined. The class of the semifields S of dimension 4 over their centres is characterized.Dedicated to A. Barlotti on the occasion of his 65. birthday.Research partially supported by G.N.S.A.G.A. (C.N.R.)     

Some new examples of flocks of Q+(3,q)

Three new examples of non-linear flocks of the non-singular ruled quadric Q⁺(3,q) of PG(3,q) are given.This paper was written while the author was a member of G.N.S.A.G.A. of C.N.R., with partial financial support from M.P.I.     

An operator-theoretic approach to theorems of the Pick-Nevanlinna and Carathéodory types

In this paper we deal with singularities of the linear systems of plane curves passing through S, where S is a zerodimensional closed subscheme of degree n of P ²=P _k ² ,k an algebraically closed field of any characteristic. We determine the least degree of a nonsingular curve passing through S, when S is in uniform position. This paper was written while the author was member of C.N.R., Sez. 3 of G.N.S.A.G.A. and was supported by M.P.I. funds     

The category of modules over a monoidal category: Abelian or not?

LetA be an algebra in an abelian monoidal category M. We prove that the category of leftA-modules is abelian, wheneverA is right coflat. This paper was written while the author was member of G.N.S.A.G.A. with partial financial support from M.I.U.R.     

Quaternionic differential forms and symplectic Pontrjagin classes

Sunto Si considerano fibrati vettoriali quaternionali dotati di connessione quaternionale e si determinano forme differenziali rappresentanti delle classi simplettiche di Pontrjagin.

---

---

Lavoro eseguito nell'ambito del gruppo G.N.S.A.G.A. del C.N.R.; esposto in una comunicazione a Oberwolfach, 7–13 Giugno 1981.     

A characterization of PGL(2, q), q odd

Following the lines of [10], we give a characterization of the group PGL(2, q), q odd, in terms of involutions.Work performed under the auspicies of G.N.S.A.C.A. of C.N.R. supported by the 40% grants of M.P.I.     

On a class of designs obtained by composition of ovaloids

Recently Tallini introduced the definition ofcomposition of two designs with suitable parameters. In this paper we study the Steiner systems obtained by composition of two given ovaloids, investigating the existence of possible Steiner subsystems of them. Furthermore we give an evaluation of the number of these Steiner systems, which are not isomorphic.In memoriam Giuseppe TalliniResearch partially supported by G.N.S.A.G.A. (C.N.R.)     

Un'osservazione sui sottoinsiemiC-analitici

Riassunto Si dà una caratterizzazione dei sottoinsiemiC-analitici di un insieme analitico reale coerente.

---

Summary A characterization ofC-analytic subsets of a coherent real analytic set is given

---

---

Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R.     

Transformation of incidence structures and sharply multiply transitive permutation sets

In this note we generalize the transformation process introduced in [8]. This generalization allows to find the nonplanar nearfield discovered by H.Karzel and W.Kerby, [5], [6], and the affine Andrè planes.Dedicated to Prof. A.Barlotti and to Prof. L.A.Rosati on their 70th birthdayWork performed under the auspicies of G.N.S.A.G.A. and supported by 40% grants of M.U.R.S.T.     

Strongly-cyclic branched coverings of knots via (g, 1)-decompositions

Strongly-cyclic branched coverings of knots are studied by using their (g, 1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups admit geometric g-words cyclic presentations. Work performed under the auspices of G.N.S.A.G.A. of I.N.d.A.M. of Italy and supported by M.U.R.S.T., by the University of Bologna, funds for selected research topics. The third named author was also supported by the INTAS project “CalcoMet-GT” 03-51-3663, the grant of RFRB, and the grant of SB RAN.     

Normal bundle to subvarieties in quadratics II

Summary In this paper we prove that the restriction of the tangent bundle of a nonsingular quadrix Q to a subvariety X is ample if and only if X does not contain a straight line. This implies that the normal bundle of a locally complete intersection, reduced and irreducible curve C is ample if and only if C is not a straight line. The result gives information also for higher dimensional subvarieties of Q.The author is member of G.N.S.A.G.A. of C.N.R.     

Stratifications et ensemble de non-cohérence d'un espace analytique réel

Sans résuméL'auteur est associé au groupe G.N.S.A.G.A. du C.N.R.     

Semi-analyticité et sous-analyticité

Summary We compare the non-Nash points set and the non semianalytic points set of a closed subanalytic set; in particular, we point out some situations in which the two sets are the same. We give some results on the structure of these sets.

---

---

Les auteurs sont associés au G.N.S.A.G.A. du C.N.R.: Recherche partiellement financiée par le M.P.I.     

Isomorfismi tra le strutture subnormali dei gruppi

Summary In this paper order-isomorphisms between subnormal structures of subsoluble groups are considered, and the images of generalized nilpotent groups in such isomorphisms are studied. A result of Pazderski about the Fitting subgroup of finite soluble groups is also extended to the upper Baer series of subsoluble groups, and an extension to infinite groups of a theorem of Heineken about isomorphisms between lattices of subnormal subgroups of finite groups is given.

---

---

Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R.     

Rami globali e parametrizzazione

Summary In this paper, using the theory of henselian rings and in particular the notion of henselian and strict henselian couples, we study the behaviour of analytic branches of an affine algebraic variety at a point x, when x varies along a singular subvariety; moreover we construct an algebraic and canonical procedure, which parametrises the branches.

---

---

Lavoro eseguito nell'ambito della sez. 3 del G.N.S.A.G.A. del C.N.R. e con il supporto finanziario del Ministero della Pubblica Istruzione.