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November 2008 Large dimensional classical groups and linear spaces
Alan R. Camina, Nick Gill, A.E. Zalesski
Bull. Belg. Math. Soc. Simon Stevin 15(4): 705-731 (November 2008). DOI: 10.36045/bbms/1225893950

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.

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Alan R. Camina. Nick Gill. A.E. Zalesski. "Large dimensional classical groups and linear spaces." Bull. Belg. Math. Soc. Simon Stevin 15 (4) 705 - 731, November 2008. https://doi.org/10.36045/bbms/1225893950

Information

Published: November 2008
First available in Project Euclid: 5 November 2008

zbMATH: 1206.05025
MathSciNet: MR2475494
Digital Object Identifier: 10.36045/bbms/1225893950

Subjects:
Primary: 05B05 , 20B25 , 20D06

Keywords: block design , finite classical group , linear space , line-transitive

Rights: Copyright © 2008 The Belgian Mathematical Society

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Vol.15 • No. 4 • November 2008
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