The Open UniversitySkip to content
 

Large dimensional classical groups and linear spaces

Camina, Alan R.; Gill, Nick and Zalesski, A. E. (2008). Large dimensional classical groups and linear spaces. Bulletin of the Belgian Mathematical Society (Simon Stevin), 15(4) pp. 705–731.

Full text available as:
[img]
Preview
PDF (Version of Record) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (266Kb) | Preview
URL: http://projecteuclid.org/euclid.bbms/1225893950
Google Scholar: Look up in Google Scholar

Abstract

Suppose that a group $G$ has socle $L$ a simple large-rank classical group. Suppose furthermore that $G$ acts transitively on the set of lines of a linear space $\mathcal{S}$. We prove that, provided $L$ has dimension at least 25, then $G$ acts transitively on the set of flags of $\mathcal{S}$ and hence the action is known. For particular families of classical groups our results hold for dimension smaller than 25.
The group theoretic methods used to prove the result (described in Section 3) are robust and general and are likely to have wider application in the study of almost simple groups acting on finite linear spaces.

Item Type: Journal Article
Copyright Holders: 2008 The Authors
ISSN: 1370-1444
Keywords: linear space; block design; line-transitive; finite classical group
Academic Unit/Department: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 28191
Depositing User: Nick Gill
Date Deposited: 16 Feb 2011 14:51
Last Modified: 06 Aug 2016 17:32
URI: http://oro.open.ac.uk/id/eprint/28191
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.

▼ Automated document suggestions from open access sources

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340   general-enquiries@open.ac.uk