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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 Subquotient ： ウィキペディア英語版 Subquotient In the mathematical fields of category theory and abstract algebra, a subquotient is a quotient object of a subobject. Subquotients are particularly important in abelian categories, and in group theory, where they are also known as sections, though this conflicts with a different meaning in category theory. For example, of the 26 sporadic groups, 20 are subquotients of the monster group, and are referred to as the "Happy Family", while the other 6 are pariah groups. A quotient of a subrepresentation of a representation (of, say, a group) might be called a subquotient representation; e.g., Harish-Chandra's subquotient theorem. ==Transitive relation== The relation »is subquotient of« is transitive. ;Proof Let $G,H,J$ groups and $\backslash phi\backslash colon\; G\backslash to\; H$ and $\backslash psi\backslash colon\; H\backslash to\; J$ be group homomorphisms, then also the composition :$\backslash psi\backslash circ\backslash phi\backslash colon\; G\backslash to\; J,\; g\; \backslash mapsto\; (\backslash psi\backslash circ\backslash phi)(g):=\backslash psi(\backslash phi(g))$ is a homomorphism. If $U$ is a subgroup of $G$ and $V$ a subgroup of $\backslash phi(U)$, then $U\text{'}:=\backslash phi^(V)$ is a subgroup of $U\backslash leq\; G$. We have $\backslash phi(U\text{'})\backslash subseteq\; V$, indeed $\backslash phi(U\text{'})=V$, because every $v\; \backslash in\; V\backslash subseteq\; \backslash phi(U)$ has a preimage in $U$. Thus $(\backslash psi\backslash circ\backslash phi)(U\text{'})=\backslash psi(V)$. This means that the image, say $\backslash psi(V)$, of a subgroup, say $V$, of $H$ is also the image of a subgroup, namely $U\text{'}$ under $\backslash psi\backslash circ\backslash phi$, of $G$. In other words: If $\backslash psi(V)$ is a subquotient of $\backslash phi(U)$ and $\backslash phi(U)$ is subquotient of $G$ then $\backslash psi(V)$ is subquotient of $G$.  ■ 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「Subquotient」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.