Line Spreads That Produce Projective Planes
We explicitly classify those line spreads of projective 5-space over a field that have the property that the given spread induces a spread in the 3-space generated by any pair of spread lines. We determine their fix groups and conclude that there exist such spreads with a trivial fix group. Also, we...
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| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/199 |
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| _version_ | 1832588099343876096 |
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| author | Hendrik Van Maldeghem |
| author_facet | Hendrik Van Maldeghem |
| author_sort | Hendrik Van Maldeghem |
| collection | DOAJ |
| description | We explicitly classify those line spreads of projective 5-space over a field that have the property that the given spread induces a spread in the 3-space generated by any pair of spread lines. We determine their fix groups and conclude that there exist such spreads with a trivial fix group. Also, we characterise regular line spreads among all line spreads of projective 3-space by their projectivity group and also by a weakening of the regularity condition. |
| format | Article |
| id | doaj-art-eb6430795851442184235936509b1c8e |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-eb6430795851442184235936509b1c8e2025-01-24T13:39:43ZengMDPI AGMathematics2227-73902025-01-0113219910.3390/math13020199Line Spreads That Produce Projective PlanesHendrik Van Maldeghem0Department of Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, BelgiumWe explicitly classify those line spreads of projective 5-space over a field that have the property that the given spread induces a spread in the 3-space generated by any pair of spread lines. We determine their fix groups and conclude that there exist such spreads with a trivial fix group. Also, we characterise regular line spreads among all line spreads of projective 3-space by their projectivity group and also by a weakening of the regularity condition.https://www.mdpi.com/2227-7390/13/2/199line spreadprojectivity groupregular spread |
| spellingShingle | Hendrik Van Maldeghem Line Spreads That Produce Projective Planes Mathematics line spread projectivity group regular spread |
| title | Line Spreads That Produce Projective Planes |
| title_full | Line Spreads That Produce Projective Planes |
| title_fullStr | Line Spreads That Produce Projective Planes |
| title_full_unstemmed | Line Spreads That Produce Projective Planes |
| title_short | Line Spreads That Produce Projective Planes |
| title_sort | line spreads that produce projective planes |
| topic | line spread projectivity group regular spread |
| url | https://www.mdpi.com/2227-7390/13/2/199 |
| work_keys_str_mv | AT hendrikvanmaldeghem linespreadsthatproduceprojectiveplanes |