A Class of Flag Transitive Planes
نویسنده
چکیده
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.
منابع مشابه
Odd order flag-transitive a‰ne planes of dimension three over their kernel
With the exception of Hering’s plane of order 27, all known odd order flag-transitive a‰ne 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 o...
متن کاملOdd 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...
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The collineation groups of even order translation planes which are cubic extensions of flag-transitive planes are determined. 2000 Mathematics Subject Classification. Primary 51E.
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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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Let $G$ be an automorphism group of a $2$-$(v,k,4)$ symmetric design $mathcal D$. In this paper, we prove that if $G$ is flag-transitive point-primitive, then the socle of $G$ cannot be an exceptional group of Lie type.
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