Abstract
By a cyclic q-clan we mean one for which there is some m modulo q + 1 for which the automorphism θ(id, M ⊗ Mm) of G⊗ given explicitly by Eq. (3.21) is a collineation of GQ(C). (See Theorem 3.8.1.) In [COP03] the authors gave a unified construction that included three previously known cyclic families plus a new one. We have modified their presentation to obtain what we call the canonical version. (See [Pa02a] for the connection between the original construction, which we do not need, and the one given here.) Moreover, we go on to show that the unified construction really does give cyclic GQ (see [CP03]).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland
About this chapter
Cite this chapter
(2007). The Cyclic q-Clans. In: q-Clan Geometries in Characteristic 2. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8508-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8508-8_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8507-1
Online ISBN: 978-3-7643-8508-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)