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Camina, Alan R.; Gill, Nick and Zalesski, A. E.
(2008).
URL: http://projecteuclid.org/euclid.bbms/1225893950
Abstract
Suppose that a group has socle
a simple large-rank classical group. Suppose furthermore that
acts transitively on the set of lines of a linear space
. We prove that, provided
has dimension at least 25, then
acts transitively on the set of flags of
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.