Cubic Extensions of Flag-transitive Planes, I. Even Order
نویسندگان
چکیده
The collineation groups of even order translation planes which are cubic extensions of flag-transitive planes are determined. 2000 Mathematics Subject Classification. Primary 51E.
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...
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 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...
متن کاملNew 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 کامل