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Subgroups of the Chevalley groups of type \(F_4\) arising from a polar space. (English) Zbl 1048.20031

The author investigates which groups arising from a polar space occur as subgroups of \(F_4(K)\), where \(K\) is a field. The paper contains a wealth of information, e.g. on the \(F_4(K)\)-geometry, polar spaces, and Moufang quadrangles. The author determines the quasisimple subgroups \(G\) of \(F_4(K)\) that are generated by a class \(\Sigma\) of abstract subgroups of \(G\) such that any member of \(\Sigma\) lies in a long root subgroup of \(F_4(K)\). She finds that a conjugate of \(G\) is contained in some classical standard subsystem subgroup of \(F_4(K)\), or \(\text{char\,}K=2\) and \(G\) arises from a Moufang quadrangle.

MSC:

20G15 Linear algebraic groups over arbitrary fields
51A50 Polar geometry, symplectic spaces, orthogonal spaces
51E12 Generalized quadrangles and generalized polygons in finite geometry
20E07 Subgroup theorems; subgroup growth
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