In mathematics, a Moufang set is a particular kind of combinatorial system named after Ruth Moufang.
Definition A Moufang set is a pair where X is a set and is a family of subgroups of the symmetric group indexed by the elements of X. The system satisfies the conditions fixes y and is simply transitive on ; Each normalises the family .
Examples Let K be a field and X the projective line P1(K) over K. Let Ux be the stabiliser of each point x in the group PSL2(K). The Moufang set determines K up to isomorphism or anti-isomorphism: an application of Hua's identity.
A quadratic Jordan division algebra gives rise to a Moufang set structure. If U is the quadratic map on the unital algebra J, let τ denote the permutation of the additive group (J,+) defined by
Then τ defines a Moufang set structure on J. The Hua maps ha of the Moufang structure are just the quadratic Ua . Note that the link is more natural in terms of J-structures.
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