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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.

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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: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 28191
Depositing User: Nick Gill
Date Deposited: 16 Feb 2011 14:51
Last Modified: 24 Feb 2016 02:57
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