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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 Base (group theory) ： ウィキペディア英語版 Base (group theory) Let $G$ be a finite permutation group acting on a set $\backslash Omega$. A sequence :$B\; =\; ()$ of ''k ''distinct elements of $\backslash Omega$ is a base for G if the only element of $G$ which fixes every $\backslash beta\_i\; \backslash in\; B$ pointwise is the identity element of $G$.〔.〕 Bases and strong generating sets are concepts of importance in computational group theory. A base and a strong generating set (together often called a BSGS) for a group can be obtained using the Schreier–Sims algorithm.〔.〕 It is often beneficial to deal with bases and strong generating sets as these may be easier to work with than the entire group. A group may have a small base compared to the set it acts on. In the "worst case", the symmetric groups and alternating groups have large bases (the symmetric group ''S''''n'' has base size ''n'' − 1), and there are often specialized algorithms that deal with these cases. ==References== 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「Base (group theory)」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.