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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 Schreier refinement theorem ： ウィキペディア英語版 Schreier refinement theorem In mathematics, the Schreier refinement theorem of group theory states that any two subnormal series of subgroups of a given group have equivalent refinements, where two series are equivalent if there is a bijection between their factor groups that sends each factor group to an isomorphic one. The theorem is named after the Austrian mathematician Otto Schreier who proved it in 1928. It provides an elegant proof of the Jordan–Hölder theorem. It is often proved using the Zassenhaus lemma. == Example == Consider $\backslash mathbb/(2)\; \backslash times\; S\_3$, where $S\_3$ is the symmetric group of degree 3. There are subnormal series : $\backslash \; \backslash times\; \backslash \; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash mathbb/(2)\; \backslash times\; \backslash \; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash mathbb/(2)\; \backslash times\; S\_3,$ : $\backslash \; \backslash times\; \backslash \; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash \; \backslash times\; S\_3\; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash mathbb/(2)\; \backslash times\; S\_3.$ $S\_3$ contains the normal subgroup $A\_3$. Hence these have refinements : $\backslash \; \backslash times\; \backslash \; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash mathbb/(2)\; \backslash times\; \backslash \; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash mathbb/(2)\; \backslash times\; A\_3\; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash mathbb/(2)\; \backslash times\; S\_3$ with factor groups isomorphic to $(\backslash mathbb/(2),\; A\_3,\; \backslash mathbb/(2))$ and : $\backslash \; \backslash times\; \backslash \; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash \; \backslash times\; A\_3\; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash \; \backslash times\; S\_3\; \backslash ;\; \backslash triangleleft\; \backslash ;\; \backslash mathbb/(2)\; \backslash times\; S\_3$ with factor groups isomorphic to $(A\_3,\; \backslash mathbb/(2),\; \backslash mathbb/(2))$. 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「Schreier refinement theorem」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.