On rank 5 projective planes
In this paper we continue the study of projective planes which admit collineation groups of low rank (Kallaher [1] and Bachmann [2,3]). A rank 5 collineation group of a projective plane ℙ of order n≠3 is proved to be flag-transitive. As in the rank 3 and rank 4 case this implies that is ℙ not desarg...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000351 |
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| _version_ | 1832567504077062144 |
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| author | Otto Bachmann |
| author_facet | Otto Bachmann |
| author_sort | Otto Bachmann |
| collection | DOAJ |
| description | In this paper we continue the study of projective planes which admit collineation groups of low rank (Kallaher [1] and Bachmann [2,3]). A rank 5 collineation group of a projective plane ℙ of order n≠3 is proved to be flag-transitive. As in the rank 3 and rank 4 case this implies that is ℙ not desarguesian and that n is (a prime power) of the form m4 if m is odd and n=m2 with m≡0mod4 if n is even. Our proof relies on the classification of all doubly transitive groups of finite degree (which follows from the classification of all finite simple groups). |
| format | Article |
| id | doaj-art-33cc22c6bd194b65a4b649608514a79c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-33cc22c6bd194b65a4b649608514a79c2025-02-03T01:01:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017232733810.1155/S0161171284000351On rank 5 projective planesOtto Bachmann0Département de mathématiques, Ecole polytechnique fédérale, Lausanne CH-1015, SwazilandIn this paper we continue the study of projective planes which admit collineation groups of low rank (Kallaher [1] and Bachmann [2,3]). A rank 5 collineation group of a projective plane ℙ of order n≠3 is proved to be flag-transitive. As in the rank 3 and rank 4 case this implies that is ℙ not desarguesian and that n is (a prime power) of the form m4 if m is odd and n=m2 with m≡0mod4 if n is even. Our proof relies on the classification of all doubly transitive groups of finite degree (which follows from the classification of all finite simple groups).http://dx.doi.org/10.1155/S0161171284000351projective planesrank 5 groups. |
| spellingShingle | Otto Bachmann On rank 5 projective planes International Journal of Mathematics and Mathematical Sciences projective planes rank 5 groups. |
| title | On rank 5 projective planes |
| title_full | On rank 5 projective planes |
| title_fullStr | On rank 5 projective planes |
| title_full_unstemmed | On rank 5 projective planes |
| title_short | On rank 5 projective planes |
| title_sort | on rank 5 projective planes |
| topic | projective planes rank 5 groups. |
| url | http://dx.doi.org/10.1155/S0161171284000351 |
| work_keys_str_mv | AT ottobachmann onrank5projectiveplanes |