𝔖 Bobbio Scriptorium
✦   LIBER   ✦

I-Transitive Ovals in Projective Planes of Odd Order

✍ Scribed by Maria Rosaria Enea; Gábor Korchmáros

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
202 KB
Volume
208
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let be a projective plane of odd order n containing an oval ⍀. We give a classification of collineation groups of which fix ⍀ and act transitively on the set I I of all internal points of ⍀.

📜 SIMILAR VOLUMES

On the Non-existence of Thas Maximal Arc
On the Non-existence of Thas Maximal Arcs in Odd Order Projective Planes
✍ A. Blokhuis; N. Hamilton; H. Wilbrink 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 91 KB

In this paper it is shown that given a non-degenerate elliptic quadric in the projective space PG(2n -1, q), q odd, then there does not exist a spread of PG(2n -1, q) such that each element of the spread meets the quadric in a maximal totally singular subspace. An immediate consequence is that the c

On arcs sharing the maximum number of po
On arcs sharing the maximum number of points with ovals in cyclic affine planes of odd order
✍ Gábor Korchmáros; Angelo Sonnino 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 187 KB 👁 2 views

## Abstract The sporadic complete 12‐arc in PG(2, 13) contains eight points from a conic. In PG(2,__q__) with __q__>13 odd, all known complete __k__‐arcs sharing exactly ½(__q__+3) points with a conic 𝒞 have size at most ½(__q__+3)+2, with only two exceptions, both due to Pellegrino, which are comp

Intersections of Hyperconics in Projecti
Intersections of Hyperconics in Projective Planes of Even Order
✍ Aiden A. Bruen; James M. McQuillan 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 204 KB

We show how to lift the even intersection equivalence relation from the hyperovals of PG(2, 4) to an equivalence relation amongst sets of hyperconics in "PG(2, F ). Here, F is any "nite or in"nite "eld of characteristic two that contains a sub"eld of order 4, but does not contain a sub"eld of order

Hyperovals in the known projective plane
Hyperovals in the known projective planes of order 16
✍ Tim Penttila; Gordon F. Royle; Michael K. Simpson 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 382 KB

We construct by computer all of the hyperovals in the 22 known projective planes of order 16. Our most interesting result is that four of the planes contain no hyperovals, thus providing counterexamples to the old conjecture that every finite projective plane contains an oval.

Parameters for Sets of Type (m, n) in Pr
Parameters for Sets of Type (m, n) in Projective Planes of Prime Power Order
✍ Mauro Biliotti; Eliana Francot 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 88 KB

A set S of k points in a projective plane of order q is of type (m, n) if each line meets S in either m or n points. The parameters are standard if q=a 2 for a=n&m. In this note we give a method for determining all admissible nonstandard parameters for a given m and q a prime power.