Subplane covered nets and semipartial geometries

✍ Scribed by F. De Clerck; N.L. Johnson

• Book ID: 103060209
• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 623 KB
• Volume: 106-107
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90539-r

✦ Synopsis

Using the characterization theorems for (semi)partiaI geometries which satisfy the diagonal axiom, we prove that subplane covered nets or equivalently (n -I)-regulus nets are isomorphic to the dual of the geometry %?:+I with point set, the set of points of a projective space H = PG(n + 1, 9) which do not belong to a fixed subspace X ^ PG(n -1, 9) and with line set, the set of lines of Askew to X. Moreover we discuss some combinatoria! problems on subplane covered nets. Some of the results are known in the literature and have group theoretic proofs, our proofs however are geometrical.