Large dimensional classical groups and linear spaces

Details Large dimensional classical groups and linear spaces Large dimensional classical groups and linear spaces

2007-01-09

arxiv.org/abs/math/0701258v2

Mathematics

Group Theory

32 pages. Version 2 has a new format that includes less repetition. It also proves a slightly stronger result; with the additi

Scientific paper

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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