✦ LIBER ✦

On a class of translation planes of square order

✍ Scribed by M.L Narayana Rao; K Satyanarayana; G Vithal Rao

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 872 KB
Volume: 66
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90130-0

No coin nor oath required. For personal study only.

✦ Synopsis

A class of translation planes of order q2, where q =pr, p is a prime, p I>7, p~=t=l (mod 10) and r is an odd natural number is constructed and the translation complements of these planes are determined. A property shared by all these planes is that the translation complement fixes a distinguished point and divides the remaining distinguished points into two orbits of lengths q and q2 _ q. The order of the translation complement is rq(q -1) 2 except for q = 7 and q = 13. The translation complements of these exceptional cases are also briefly studied. The class of planes considered in this paper are distinct from the classes of translation planes of S.D. Cohen and M.J. Ganley [Quart. J. Math. Oxford, 35 (1984) 101-113].

📜 SIMILAR VOLUMES

On a class of derived translation planes

On a class of derived translation planes of square order

✍ M.L. Narayana Rao; K. Satyanarayana; G. Vithal Rao 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 725 KB

Translation Laguerre Planes of Order 16

✍ D.G. Glynn; G.F. Steinke 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 434 KB

Translation Laguerre planes of order 16 are investigated, and a related search is carried out for translation ovals in the eight translation planes of order 16 and for certain collections of such ovals called 2-pencils. Although in some of these planes there are considerably more translation hyperov

Large quartic groups on translation plan

Large quartic groups on translation planes, II—Even order: Characterization of the Ott-Schaeffer planes

✍ Mauro Biliotti; Vikram Jha; Norman L. Johnson 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 158 KB

## Abstract A general theory of collineation groups generated by quartic groups of even order is considered. Applications are given to collineation groups generated by ‘large’ quartic groups. © 2005 Wiley Periodicals, Inc. J Combin Designs 13: 195–210, 2005.

Translation planes of order q3 which adm

Translation planes of order q3 which admits SL(2, q)

✍ C Bartolone; T.G Ostrom 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 484 KB

On a class of square-free graphs

✍ Xue Qingbo 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 171 KB

On groups of Baer collineations acting o

On groups of Baer collineations acting on cartesian and translation planes

✍ Vikram Jha 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 931 KB