A characterization of translation planes and dual translation planes of characteristic \(\neq 2\) (Q1333604)
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scientific article; zbMATH DE number 639571
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of translation planes and dual translation planes of characteristic \(\neq 2\) |
scientific article; zbMATH DE number 639571 |
Statements
A characterization of translation planes and dual translation planes of characteristic \(\neq 2\) (English)
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15 September 1994
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Generalizing a definition of \textit{A. Wagner} [Math. Z. 87, 1--11 (1965; Zbl 0131.36804)] the author calls an affine plane a weak \(W\)-plane if a collineation group \(G\) contains for every affine flag \((Q, \ell)\) an involutory homology fixing this flag. Even with this weaker condition the result of Wagner can be improved: Any finite weak \(W\)-plane is a translation plane or a dual translation plane of characteristic \(\neq 2\).
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finite projective plane
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nearfield
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involutory homology
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finite weak \(W\)-plane
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translation plane
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