A new flag transitive affine plane of order $27$
نویسندگان
چکیده
منابع مشابه
New Flag-Transitive Affine Planes of Even Order
At least [6 n&1 1 (q i+1)] qn 2m1 log2 q of these planes have kernel GF(q). Moreover, we construct 7(mi)6i q mi planes, where the sum is over all sequences (mi) behaving as in the theorem; and then we settle the isomorphism problem for these planes (Theorem 5.2). The proof combines methods in [Wi] and [Ka]: these planes arise from symplectic and orthogonal spreads combined with changing from fi...
متن کاملNearly flag-transitive affine planes
Spreads of orthogonal vector spaces are used to construct many translation planes of even order q, for odd m > 1, having a collineation with a (q − 1)-cycle on the line at infinity and on each of two affine lines.
متن کاملTwo Families of Flag-transitive Affine Planes
Two families of flag-transitive nondesarguesian affine planes of odd order are defined, and isomorphisms among the various planes are studied. Thir ty years ago Wagner [5] proved the impor tan t result that every finite flag-transitive affine plane is a t ranslat ion plane. However , since that t ime relatively few classes of such planes have been found. The purpose of this note is to c o m m e...
متن کاملFlag-transitive Extensions of Dual Affine Planes
(with 1 , q , ̀ ) . An infinite family of simply connected examples for this diagram with q 5 2 is obtained by truncating Coxeter complexes of type D n . Two dif ferent finite families with three members and q 5 4 arise from the Steiner systems for the Mathieu groups M 2 2 , M 2 3 and M 2 4 . The geometries of these two families are simply connected . Three more simply connected examples of rank...
متن کاملA construction of one-dimensional affine flag-transitive linear spaces
The finite flag-transitive linear spaces which have an insoluble automorphism group were given a precise description in [BDD+90], and their classification has recently been completed (see [Lie98] and [Sax02]). However, the remaining case where the automorphism group is a subgroup of one-dimensional affine transformations has not been classified and bears a variety of known examples. Here we giv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0420427-8