Abstract
Let π be a translation plane of order q 4 admitting a collineation group G isomorphic to SL(2, q), p r = q, in the translation complement. It is shown that if the p-elements of G are elations and L is an elation axis then the kernel of π is GF( q) and G acts 1 2 - transitive on l ∞− N∩l ∞ (where N denotes the elation net) if and only if there is a regular parallelism of L (considering L as PG(3, q)). With no assumption on the p-elements, it is shown that the existence SL(2, q)× z 1+ q+ q 2 as a collineation group implies that the p-elements are elations, the kernel is GF( q) and any elation axis L admits a regular parallelism as PG(3, q).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
