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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mathieu groupoid ： ウィキペディア英語版 Mathieu groupoid In mathematics, the Mathieu groupoid M13 is a groupoid acting on 13 points such that the stabilizer of each point is the Mathieu group M12. It was introduced by and studied in detail by . ==Construction== The projective plane of order 3 has 13 points and 13 lines, each containing 4 points. The Mathieu groupoid can be visualized as a sliding block puzzle by placing 12 counters on 12 of the 13 points of the projective plane. A move consists of moving a counter from any point ''x'' to the empty point ''y'', then exchanging the 2 other counters on the line containing ''x'' and ''y''. The Mathieu groupoid consists of the permutations that can be obtained by composing several moves. This is not a group because two operations ''A'' and ''B'' can only be composed if the empty point after carrying out ''A'' is the empty point at the beginning of ''B''. It is in fact a groupoid (a category such that every morphism is invertible) whose 13 objects are the 13 points, and whose morphisms from ''x'' to ''y'' are the operations taking the empty point from ''x'' to ''y''. The morphisms fixing the empty point form a group isomorphic to the Mathieu group M12 with 12×11×10×9×8 elements. 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「Mathieu groupoid」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.