Abstract
In this note, we investigate finite connected flat geometries of type C 3 of uniform odd order in which the lines and the planes form a projective space. We give an algebraic description of such geometries by sets of alternating bilinear forms or, equivalently, by sets of skew symmetric matrices. These sets of skew symmetric matrices will be identified in a natural way with the full point set of a projective plane. By a general result concerning two-valued functions defined on projective planes of order 5, we finally prove the non-existence of finite connected flat geometries of type C 3 of uniform order 5 in which the lines and the planes form a projective space.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.