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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 Quaternion group ： ウィキペディア英語版 Quaternion group In group theory, the quaternion group is a non-abelian group of order eight, isomorphic to a certain eight-element subset of the quaternions under multiplication. It is often denoted by Q or Q8, and is given by the group presentation :$\backslash mathrm\; =\; \backslash langle\; -1,i,j,k\; \backslash mid\; (-1)^2\; =\; 1,\; \backslash ;i^2\; =\; j^2\; =\; k^2\; =\; ijk\; =\; -1\; \backslash rangle,\; \backslash ,\backslash !$ where 1 is the identity element and −1 commutes with the other elements of the group. == Compared to dihedral group == The Q8 group has the same order as the dihedral group D4, but a different structure, as shown by their Cayley and cycle graphs: The dihedral group D4 arises in the split-quaternions in the same way that Q8 lies in the quaternions. 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「Quaternion group」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.