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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 Opposite group ： ウィキペディア英語版 Opposite group In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action. == Definition == Let $G$ be a group under the operation $$ *. The opposite group of $G$, denoted $G^$, has the same underlying set as $G$, and its group operation $\backslash mathbin$ is defined by $g\_1\; \backslash mathbin\; g\_2\; =\; g\_2$ * g_1. If $G$ is abelian, then it is equal to its opposite group. Also, every group $G$ (not necessarily abelian) is naturally isomorphic to its opposite group: An isomorphism $\backslash varphi:\; G\; \backslash to\; G^$ is given by $\backslash varphi(x)\; =\; x^$. More generally, any anti-automorphism $\backslash psi:\; G\; \backslash to\; G$ gives rise to a corresponding isomorphism $\backslash psi\text{'}:\; G\; \backslash to\; G^$ via $\backslash psi\text{'}(g)=\backslash psi(g)$, since : $\backslash psi\text{'}(g$ * h) = \psi(g * h) = \psi(h) * \psi(g) = \psi(g) \mathbin \psi(h)=\psi'(g) \mathbin \psi'(h). 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「Opposite 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.