The geometry of GL(2,q) in translation planes of even order q2
In this article we show the following: Let π be a translation plane of even order q2 that admits GL(2,q) as a collineation group. Then π is either Desarguesian, Hall or Ott-Schaeffer.
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| Format: | Article |
| Language: | English |
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Wiley
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171278000459 |
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| _version_ | 1832563101066592256 |
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| author | N. L. Johnson |
| author_facet | N. L. Johnson |
| author_sort | N. L. Johnson |
| collection | DOAJ |
| description | In this article we show the following: Let π be a translation plane of even order q2 that admits GL(2,q) as a collineation group. Then π is either Desarguesian, Hall or Ott-Schaeffer. |
| format | Article |
| id | doaj-art-8765bc89d5dc4e5d95e35338a8ffe3f7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8765bc89d5dc4e5d95e35338a8ffe3f72025-02-03T01:21:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011444745810.1155/S0161171278000459The geometry of GL(2,q) in translation planes of even order q2N. L. Johnson0Department of Mathematics, The University of Iowa, Iowa City 52242, Iowa, USAIn this article we show the following: Let π be a translation plane of even order q2 that admits GL(2,q) as a collineation group. Then π is either Desarguesian, Hall or Ott-Schaeffer.http://dx.doi.org/10.1155/S0161171278000459translation planesDesarguesianHallOtt-Schaeffer planes. |
| spellingShingle | N. L. Johnson The geometry of GL(2,q) in translation planes of even order q2 International Journal of Mathematics and Mathematical Sciences translation planes Desarguesian Hall Ott-Schaeffer planes. |
| title | The geometry of GL(2,q) in translation planes
of even order q2 |
| title_full | The geometry of GL(2,q) in translation planes
of even order q2 |
| title_fullStr | The geometry of GL(2,q) in translation planes
of even order q2 |
| title_full_unstemmed | The geometry of GL(2,q) in translation planes
of even order q2 |
| title_short | The geometry of GL(2,q) in translation planes
of even order q2 |
| title_sort | geometry of gl 2 q in translation planes of even order q2 |
| topic | translation planes Desarguesian Hall Ott-Schaeffer planes. |
| url | http://dx.doi.org/10.1155/S0161171278000459 |
| work_keys_str_mv | AT nljohnson thegeometryofgl2qintranslationplanesofevenorderq2 AT nljohnson geometryofgl2qintranslationplanesofevenorderq2 |