Affine planes admitting a collineation group with a transitive action on the line at infinity
نویسندگان
چکیده
منابع مشابه
Finite 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...
متن کاملA Note on Tangentially Transitive Affine Planes
Let $1 be a finite affine translation plane. If 21 contains a subplane, collineation group pair (2I0, A) such that: * A leaves each point of 2t0 fixed and acts transitively on the points of / \ { / n 2I0}, for / a line of 21 with / n 2l0 a line of 2l0, then 21 is said to be tangentially transitive with respect to 2l0. Jha in his thesis [3] has proved that if 21 is tangentially transitive with r...
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We investigate finite elation Laguerre planes admitting a group of automorphisms that is two-transitive on the set of generators. We exclude the sporadic cases of socles in two-transitive groups, as well as the cases with abelian socle (except for the smallest ones, where the Laguerre planes are Miquelian of order at most four). The remaining cases are dealt with in a separate paper. As a conse...
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 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,...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.01.033