Nearly flag-transitive affine planes
نویسندگان
چکیده
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.
منابع مشابه
Odd order flag-transitive affine planes of dimension three over their kernel
With the exception of Bering's plane of order 27, all known odd order flag-transitive affine planes are one of two types: admitting a cyclic transitive action on the line at infinity, or admitting a transitive action on the line at infinity with two equal-sized cyclic orbits. In this paper we show that when the dimension over the kernel for these planes is three, then the known examples are the...
متن کاملA Class of Flag Transitive Planes
A class of translation affine planes of order q2, where q is a power of a prime/>>3 is constructed. These planes have an interesting property that their collineation groups are flag transitive.
متن کاملA Note on Some Flag-Transitive Affine Planes
Relatively few finite non desarguesian flag-transitive affine planes are known whose collineation groups are solvable. With a single exception (see below), all of the known ones of odd order fall into two families studied in [Ka, Su l ] ; those references also contain some historical remarks. The purpose of this note is to construct an additional family of such planes, explain why they are new,...
متن کاملFinite flag-transitive affine planes with a solvable automorphism group
In this paper, we consider finite flag-transitive affine planes with a solvable automorphism group. Under a mild number-theoretic condition involving the order and dimension of the plane, the translation complement must contain a linear cyclic subgroup that either is transitive or has two equal-sized orbits on the line at infinity. We develop a new approach to the study of such planes by associ...
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تاریخ انتشار 2009