Transition planes constructed from semifield planes
نویسندگان
چکیده
منابع مشابه
The six semifield planes associated with a semifield flock
In 1965 Knuth [17] noticed that a finite semifield was determined by a 3-cube array (aijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f, g) where f and g are functions from GF (q) to GF (q) with the property that f and g are linear over some subfield an...
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In this article we investigate the autotopism group of the so-called cyclic semifield planes. We show that the group generated by the homology groups of the nuclei is already the full group of autotopisms that are linear with respect to the nuclei. The full autotopism group is also computed with the exception of one special subcase.
متن کاملNew Semifield Planes of order 81 ∗
A finite semifield D is a finite nonassociative ring with identity such that the set D∗ = D \ {0} is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield planes of order 81 by means of computational methods. These computer-assisted results yield to a complete classification (up to isotopy) of 81-element finite semifields.
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A finite semifield D is a finite nonassociative ring with identity such that the set D∗ = D \ {0} is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield planes of orders 64 and 81 by means of computational methods. These computer-assisted results yield to a complete classification (up to isotopy) of 81-element finite s...
متن کاملReconstructing Projective Planes from Semibiplanes
From a projective plane Π with a homology τ of order 2, one obtains an incidence system having as points and blocks the 〈τ〉-orbits of length 2 on the points and lines of Π, and with incidence inherited from Π. The resulting structure, denoted by Π/τ , is an example of a homology semibiplane. We have shown that a Desarguesian projective plane of odd prime order is uniquely reconstructible from i...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1971
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1971.36.701