Details

Autor(en) / Beteiligte

• Johnson, N. L.

Titel

Partially sharp subsets of PΓL(n, q)

Ist Teil von

• Finite Geometries and Combinatorics, 1993, Vol.Series Number 191, p.217-232

Ort / Verlag

United States: Cambridge University Press

Erscheinungsjahr

1993

Link zum Volltext

Quelle

Cambridge University Press online books

Beschreibungen/Notizen

• AbstractIn this article, certain translation nets which are unions of subplane covered nets are shown to be equivalent to partially sharp subsets of PFZ(n, q). In particular, translation planes of order q2 and arbitrary kernel that admit two distinct Baer groups of order q–1 with identical component orbits are shown to be equivalent to partially sharp subsets of cardinality q of PTL(2, K) for some field K isomorphic to GF(q).IntroductionRecently, a number of various connections have been established between translation planes and other geometric or combinatorial incidence structures. In particular, there are connections between flocks of hyperbolic quadrics in PG(3, q) and translation planes with spreads in PG(3, q) such that the spread is a union of reguli that share two lines. Similarly, partial flocks correspond to translation nets whose partial spreads are unions of reguli that share two lines.It is well known that a Miquelian Minkowski plane can be defined using a hyperbolic quadric in PG(3, q) and when this connection is made, the points of the Minkowski plane are identified with the elements of PG(1, q) × PG(1, q), the circles (conies) correspond to the elements of PGL(2, q) and a flock corresponds to a sharply transitive subset of PGL(2, q).