Polynomial Moulton Planes

Year 1977, Volume: 26 , 0 - 0, 01.01.1977

Rüstem Kaya

https://doi.org/10.1501/Commua1_0000000274

Cited By: 1

Abstract

In this paper a family of affine planes is defined. Any plane in the family is deter- mined fay a tripîe (F, 0, n) consisting of a pseudo-ordered field F, a one-to-one and order reversing or order preserving function 0 of F onto itself, and an element n of the set N,= {2x: xgN the set of positive integers} if0 is order reversing or an element n of either of the sets Nı= e N} and N3— |(2x-l)~^;x e N} if 0 is order preserving. In the case where F is a finite field of order q if n e Ng then (q-l, n)=2 and the elements a and -a are not both square or non-square elements in the field F; if n e Nj or n e N3 then (q-l, n)=l or (q-l, n“9—I r®sp®<^t^vely. These planes are non-desarguesian for every n and every F unless 0 (x) = ax+ p, where a e F but P {o} or a e P according as n e Nj or n e Nık^Na; e F, (P is the multiplicative subgroup of index 2 of F).
For n=0 the planes in the family are the so-called Moulton planes.

Keywords

Polynomial Moulton, Planes, Statistics

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi