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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1984-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000351 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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). |
|---|---|
| ISSN: | 0161-1712 1687-0425 |