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Quasigroups --- Group theory --- Group theory. --- Quasigroups.

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Quasigroups --- Group theory

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Algebra, Universal --- Group theory. --- Quasigroups. --- Algèbre universelle. --- Analyse combinatoire --- Géometrie --- Groupes, Théorie des --- Lie, Algèbres de --- Quasigroupes. --- Algèbre universelle. --- Géometrie --- Lie, Algèbres de

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"A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. We extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, we show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. We also obtain explicit formulas for the root groups, the T-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups"--

Lie algebras. --- Jordan algebras. --- Linear algebraic groups. --- Lie, Algèbres de. --- Jordan, Algèbres de. --- Groupes algébriques linéaires. --- Division algebras. --- Moufang loops. --- Combinatorial group theory. --- Algèbre à division --- Moufang, Boucles de --- Algèbres de Jordan --- Théorie combinatoire des groupes --- Division algebras --- Moufang loops --- Jordan algebras --- Combinatorial group theory --- Combinatorial groups --- Groups, Combinatorial --- Combinatorial analysis --- Group theory --- Algebra, Abstract --- Algebras, Linear --- Loops, Moufang --- Loops (Group theory) --- Algebras, Division --- Algebraic fields --- Quasigroups --- Rings (Algebra)