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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 Normal form for free groups and free product of groups ： ウィキペディア英語版 Normal form for free groups and free product of groups In mathematics, particularly in combinatorial group theory, a normal form for a free group over a set of generators or for a free product of groups is a representation of an element by a simpler element, the element being either in the free group or free products of group. In case of free group these simpler elements are reduced words and in the case of free product of groups these are reduced sequences. The precise definitions of these are given below. As it turns out, for a free group and for the free product of groups, there exists a unique normal form i.e each element is representable by a simpler element and this representation is unique. This is the Normal Form Theorem for the free groups and for the free product of groups. The proof here of the Normal Form Theorem follows the idea of Artin and van der Waerden. ==Normal form for free groups== Let $G$ be a free group with generating set $S$. Each element in $G$ is represented by a word $w$, $w=a\_1a\_2\backslash ldots\backslash ,a\_n$, where $a\_j\backslash in\backslash ,S^\backslash ,\backslash forall\backslash ,1\backslash leq\backslash ,j\backslash leq\backslash ,n.$ 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「Normal form for free groups and free product of groups」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.