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In mathematics, Moufang polygons are a generalization by Jacques Tits of the Moufang planes studied by Ruth Moufang, and are irreducible buildings of rank two that admit the action of root groups. In a book on the topic, Tits and Weiss classify them all. An earlier theorem, proved independently by Tits and Weiss,〔 51 (3), (1979) 267–269 .〕 showed that a Moufang polygon must be a generalized 3-gon, 4-gon, 6-gon, or 8-gon, so the purpose of the aforementioned book was to analyze these four cases. ==Definitions== *A generalized ''n''-gon is a bipartite graph of diameter ''n'' and girth 2''n''. *A graph is called thick if all vertices have valence at least 3. *A root of a generalized ''n''-gon is a path of length ''n''. *An apartment of a generalized ''n''-gon is a cycle of length 2''n''. *The root subgroup of a root is the subgroup of automorphisms of a graph that fix all vertices adjacent to one of the inner vertices of the root. *A Moufang ''n''-gon is a thick generalized ''n''-gon (with ''n''>2) such that the root subgroup of any root acts transitively on the apartments containing the root. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Moufang polygon」の詳細全文を読む スポンサード リンク
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