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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 Strong generating set ： ウィキペディア英語版 Strong generating set In abstract algebra, especially in the area of group theory, a strong generating set of a permutation group is a generating set that clearly exhibits the permutation structure as described by a stabilizer chain. A stabilizer chain is a sequence of subgroups, each containing the next and each stabilizing one more point. Let $G\; \backslash leq\; S\_n$ be a group of permutations of the set $\backslash .$ Let :$B\; =\; (\backslash beta\_1,\; \backslash beta\_2,\; \backslash ldots,\; \backslash beta\_r)$ be a sequence of distinct integers, $\backslash beta\_i\; \backslash in\; \backslash \; ,$ such that the pointwise stabilizer of $B$ is trivial (i.e., let $B$ be a base for $G$). Define :$B\_i\; =\; (\backslash beta\_1,\; \backslash beta\_2,\; \backslash ldots,\; \backslash beta\_i),\backslash ,$ and define $G^$ to be the pointwise stabilizer of $B\_i$. A strong generating set (SGS) for G relative to the base $B$ is a set :$S\; \backslash subseteq\; G$ such that :$\backslash langle\; S\; \backslash cap\; G^\; \backslash rangle\; =\; G^$ for each $i$ such that $1\; \backslash leq\; i\; \backslash leq\; r$. The base and the SGS are said to be ''non-redundant'' if :$G^\; \backslash neq\; G^$ for $i\; \backslash neq\; j$. A base and strong generating set (BSGS) for a group can be computed using the Schreier–Sims algorithm. ==References== * A. Seress, ''Permutation Group Algorithms'', Cambridge University Press, 2002. 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「Strong generating set」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.