On the non-existence of a projective plane of order 15 with an \(A_4\)-invariant oval (Q704275)
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scientific article; zbMATH DE number 2127149
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the non-existence of a projective plane of order 15 with an \(A_4\)-invariant oval |
scientific article; zbMATH DE number 2127149 |
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On the non-existence of a projective plane of order 15 with an \(A_4\)-invariant oval (English)
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13 January 2005
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Let \(\pi\) be a projective plane of order 15 with an oval \(\Omega\). Assume \(\pi\) admits a collineation group \(G\) fixing \(\Omega\) such that \(G\) is isomorphic to \(A_4\) and the action of \(G\) on \(\Omega\) yields precisely two orbits \(\Omega_1\) and \(\Omega_2\) with \(|\Omega_2|=4\). We prove that the Buekenhout oval arising from \(\Omega\) cannot exist.
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Oval
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Collineation group
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Homology
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Buekenhout oval
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