On rank 4 projective planes
Let a finite projective plane be called rank m plane if it admits a collineation group G of rank m, let it be called strong rank m plane if moreover GP=G1 for some point-line pair (P,1). It is well known that every rank 2 plane is desarguesian (Theorem of Ostrom and Wagner). It is conjectured that t...
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000185 |
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| _version_ | 1849696391675248640 |
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| author | O. Bachmann |
| author_facet | O. Bachmann |
| author_sort | O. Bachmann |
| collection | DOAJ |
| description | Let a finite projective plane be called rank m plane if it admits a collineation group G of rank m, let it be called strong rank m plane if moreover GP=G1 for some point-line pair (P,1). It is well known that every rank 2 plane is desarguesian (Theorem of Ostrom and Wagner). It is conjectured that the only rank 3 plane is the plane of order 2. By [1] and [7] the only strong rank 3
plane is the plane of order 2. In this paper it is proved that no strong rank 4 plane exists. |
| format | Article |
| id | doaj-art-c81ac9a5e5a94e2ba83e2fe4c495e84f |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c81ac9a5e5a94e2ba83e2fe4c495e84f2025-08-20T03:19:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014230531910.1155/S0161171281000185On rank 4 projective planesO. Bachmann0Département de mathématiques, Ecole polytechnique fédérale, Lausanne CH-1007, SwazilandLet a finite projective plane be called rank m plane if it admits a collineation group G of rank m, let it be called strong rank m plane if moreover GP=G1 for some point-line pair (P,1). It is well known that every rank 2 plane is desarguesian (Theorem of Ostrom and Wagner). It is conjectured that the only rank 3 plane is the plane of order 2. By [1] and [7] the only strong rank 3 plane is the plane of order 2. In this paper it is proved that no strong rank 4 plane exists.http://dx.doi.org/10.1155/S0161171281000185projective planesrank 4 groups. |
| spellingShingle | O. Bachmann On rank 4 projective planes International Journal of Mathematics and Mathematical Sciences projective planes rank 4 groups. |
| title | On rank 4 projective planes |
| title_full | On rank 4 projective planes |
| title_fullStr | On rank 4 projective planes |
| title_full_unstemmed | On rank 4 projective planes |
| title_short | On rank 4 projective planes |
| title_sort | on rank 4 projective planes |
| topic | projective planes rank 4 groups. |
| url | http://dx.doi.org/10.1155/S0161171281000185 |
| work_keys_str_mv | AT obachmann onrank4projectiveplanes |