A characterization of the desarguesian planes of order q2 by SL(2,q)
The main result is that if the translation complement of a translation plane of order q2 contains a group isomorphic to SL(2,q) and if the subgroups of order q are elations (shears), then the plane is Desarguesian. This generalizes earlier work of Walker, who assumed that the kernel of the plane con...
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000551 |
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| _version_ | 1832551304868659200 |
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| author | D. A. Foulser N. L. Johnson T. G. Ostrom |
| author_facet | D. A. Foulser N. L. Johnson T. G. Ostrom |
| author_sort | D. A. Foulser |
| collection | DOAJ |
| description | The main result is that if the translation complement of a translation plane of order q2 contains a group isomorphic to SL(2,q) and if the subgroups of order q are elations (shears), then the plane is Desarguesian. This generalizes earlier work of Walker, who assumed that the kernel of the plane contained GF(q). |
| format | Article |
| id | doaj-art-169a152da991467ebfb27c9ae135c316 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-169a152da991467ebfb27c9ae135c3162025-02-03T06:01:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016360560810.1155/S0161171283000551A characterization of the desarguesian planes of order q2 by SL(2,q)D. A. Foulser0N. L. Johnson1T. G. Ostrom2Mathematics Department, University of Illinois at Chicago Circle, Chicago, Illinois 60680, USADepartment of Mathematics, The University of Iowa, lowa City, Iowa 52242, USADepartment of Pure and Applied Mathematics, Washington State University, Pullman, Washington 99164, USAThe main result is that if the translation complement of a translation plane of order q2 contains a group isomorphic to SL(2,q) and if the subgroups of order q are elations (shears), then the plane is Desarguesian. This generalizes earlier work of Walker, who assumed that the kernel of the plane contained GF(q).http://dx.doi.org/10.1155/S0161171283000551translation planestranslation complementelations. |
| spellingShingle | D. A. Foulser N. L. Johnson T. G. Ostrom A characterization of the desarguesian planes of order q2 by SL(2,q) International Journal of Mathematics and Mathematical Sciences translation planes translation complement elations. |
| title | A characterization of the desarguesian planes of order q2 by SL(2,q) |
| title_full | A characterization of the desarguesian planes of order q2 by SL(2,q) |
| title_fullStr | A characterization of the desarguesian planes of order q2 by SL(2,q) |
| title_full_unstemmed | A characterization of the desarguesian planes of order q2 by SL(2,q) |
| title_short | A characterization of the desarguesian planes of order q2 by SL(2,q) |
| title_sort | characterization of the desarguesian planes of order q2 by sl 2 q |
| topic | translation planes translation complement elations. |
| url | http://dx.doi.org/10.1155/S0161171283000551 |
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