Polynomial Moulton Planes

Authors : Rüstem KAYA

Pages : 0-0

Doi:10.1501/Commua1_0000000274

View : 14 | Download : 8

Publication Date : 1977-01-01

Article Type : Research Paper

Abstract :In this paper a family of affine planes is defined. Any plane in the family is deter- mined fay a tripîe insert ignore into journalissuearticles values(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— |insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(q-l, n);=l or insert ignore into journalissuearticles values(q-l, n“9—I r®sp®<^t^vely. These planes are non-desarguesian for every n and every F unless 0 insert ignore into journalissuearticles values(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, insert ignore into journalissuearticles values(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