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Transition planes
constructed from semifield planes
Norman Lloyd Johnson |
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Vol. 36 (1971), No. 3, 701–711
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Abstract |
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Let π be an affine plane of order q2 that is coordinatized by a “derivable” semifield 𝒮 = (𝒮,+,⋅). If (𝒮,+) is a right vector space over F = GF(q) then a plane π′ may be constructed from π using Ostrom’s method of “derivation.” The purpose of this article is to examine the planes π′ and their coordinate structures (𝒮,+,∗). It is shown, in particular, that (𝒮,+,∗) is a (right) quasifield which is neither a nearfield nor a semifield. Furthermore, it is shown that π′ is always of Lenz-Barlotti class IVa. 1. The automorphism groups of semifields of square order are also briefly investigated. |
Mathematical Subject Classification
Primary: 50.70
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Milestones
Received: 3 June 1970
Published: 1 March 1971
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Authors |
| Norman Lloyd Johnson | |
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