A Note on Some Flag-Transitive Affine Planes
نویسندگان
چکیده
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, and estimate how many pairwise nonisomorphic planes are obtained by this construction.
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...
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متن کاملOn primitivity and reduction for flag-transitive symmetric designs
We present some results on flag-transitive symmetric designs. First we see what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group. Then we move on to study the possibilities for a primitive, flag-transitive automorphism group, and prove that for λ ≤ 3, the group must be affine or almost simple, and finally we analyse the case in which a ...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 65 شماره
صفحات -
تاریخ انتشار 1994