1,721,012 research outputs found
Inversive planes, Minkowski planes and regular sets of points
Full text linkNew examples of regular sets of points for the Miquelian inversive planes of order q, q a prime power, q greater than or equal to 7, are found and connections between such planes and certain Minkowski planes of order q(2) are presented
Finite Minkowski Planes and embedded Inversive Planes
No full textIt is proved that each known finite Minkowski plane of order p^m, with p prime and m even, contains embedded Miquelian inversive planes
Key distribution patterns using tangent circle structures
No full textThe problem of key management in a communications network is of primary importance. A key distribution pattern is an incidence structure which provides a secure method of distributing keys in a large network reducing storage requirements. It is of interest to find explicit constructions for key distribution patterns. In some paper of C. O'Keefe, examples are shown using the finite circle geometries (Minkowski, Laguerre and inversive planes); in a paper of K. Quinn examples are constructed from conics in finite projective and affine planes. In this paper, we construct some examples using the finite tangent-circle structures, introduced in a paper of Quattrocchi and Rinaldi (1988) and we give a comparison of the storage requirements
Transformation of incidence structures and sharply multiply transitive permutation sets
No full textThe transformation process introduced in [P. Quattrocchi, L.A.Rosati "Transformation of designs and other incidence structures" Geom. ded. (1992), 233-240] is generalized. This generalization allows to construct examples of non-planar nearfileds and to construct the class of finite André planes by transformation of the desarguesian ones
Nilpotent 1-factorizations of the complete graph
No full textFor which groups G of even order 2n does a 1-factorization of the complete graph on 2n veritces exist with the property of admitting G as a sharply vertex-transitive automorphism group? The complete answer is still unknown. Using the definition of a starter in G introduced in [M. Buratti "Abelian 1-factorizations of the complete graph" Europ. J Comb. 2001, pp.291-295], we give a positive answer for new classes of groups; for example, the nilpotent groups with either an abelian Sylow 2-subgroup or a non-abelian Sylow 2-subgroup which possesses a cyclic subgroup of index 2. Further considerations are given in case the automorphism group G fixes a 1-factor
A characterization of PGL(2,q), q odd
No full textA characterization of the projective linear group PGL(2,q) is given in term of involutions
Vertex-regular 1-factorizations of the complete graph
No full textA 1-factorization of a complete graph is said to be regular if it admits an automorphism group with a sharply transitive action on the vertex set. Which abstract groups can realize such a situation? The complete answer is still unknown but the problem has been solved in some cases. We illustrate the state of art
Arcs in the Hall Planes
No full textUsing a transformation tecnique for designs introduced in [P.Quattrocchi, L.A.Rosati "Transformation of designs and other incidence structures" Geom. Ded. (1992), 233-240], a class of arcs embeddable both in the Hall plane of order q^2 (q a prime power) and in its dual is constructedand. These arcs are complete in the unital of Gruning
Construction of Unitals in the Hall Planes
No full textUsing a transformation method for incidence structures introduced in [P.Quattrocchi, L.A.Rosati "Transformation of designs and other incidence structures" Geom. ded. 44 (1992), 233-240] I construct unitals embedded in the Hall planes by transformation of the Buekenhout-Metz unitals
Hyperbolic unitals in the Hall planes
No full textUsing the transformation tecnique introduced in [P. Quattrocchi, L.A. Rosati "Transformation of designs and other incidence structres" Geom. Ded. (1992), 233-240], some sufficient conditions to transform a unital embedded in a projective plane into another one are given. As application unitals in the Hall planes are constructed by transformation of the hermitian curves. Necessary and sufficient conditions for the constructed unitals to be projectively equivalent are given too and fferent classes of not projectively equivalent Buekenhout's unitals are found in this manner. The unital of Gruning in the Hall plane is reconstructed and its embeddability in the dual of the Hall plane is also proved. Finally it is proved that the affine unital associated to the unital of Gruning is ismorphic to the hyperbolic hermitian curve
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