Special Moufang sets, their root groups and their {micro}-maps |
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Authors: | De Medts Tom; Segev Yoav; Tent Katrin |
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Institution: | Department of Pure Mathematics and Computer Algebra Ghent University Krijgslaan 281 S22 9000 Gent Belgium |
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Abstract: | We prove Timmesfeld's conjecture that special abstract rankone groups are quasisimple. We give two characterizations ofthe root groups in special Moufang sets: a normal subgroup ofthe point stabilizer is a root group if it is either regular,or nilpotent and transitive. We prove that if a root group ofa special Moufang set contains an involution, then it is ofexponent 2. We also show that the root groups are abelian ifand only if the so-called µ-maps are involutions. |
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