Gill, Nick
(2007).

PDF (Version of Record)
 Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (170Kb) 
URL:  http://nzjm.math.auckland.ac.nz/index.php/Polar_Sp... 

Google Scholar:  Look up in Google Scholar 
Abstract
Given polar spaces (V,β) and (V,Q) where V is a vector space over a field K, β a reflexive sesquilinear form and Q a quadratic form, we have associated classical isometry groups. Given a subfield F of K and an Flinear function L : K → F we can define new spaces (V,Lβ) and (V,LQ) which are polar spaces over F.
The construction so described gives an embedding of the isometry groups of (V,β) and (V,Q) into the isometry groups of (V,Lβ) and (V,LQ).In the finite field case under certain added restrictions these subgroups are maximal and form the so called field extension subgroups of Aschbacher's class C_{3}.
We give precise descriptions of the polar spaces so defined and their associated isometry group embeddings. In the finite field case our results give extra detail to the account of maximal field extension subgroups given by Kleidman and Liebeck.
Item Type:  Journal Article 

Copyright Holders:  2007 The Author 
Academic Unit/Department:  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) 
Item ID:  28190 
Depositing User:  Nick Gill 
Date Deposited:  17 Feb 2011 12:08 
Last Modified:  07 Oct 2016 01:57 
URI:  http://oro.open.ac.uk/id/eprint/28190 
Share this page: 
Download history for this item
These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.