翻訳と辞書 Words near each other ・ Double Cola ・ Double Commander ・ Double compare-and-swap ・ Double concerto ・ Double Concerto (Brahms) ・ Double Concerto (Delius) ・ Double Concerto for Two String Orchestras, Piano, and Timpani (Martinů) ・ Double cone ・ Double cone (biology) ・ Double Confession ・ Double consciousness ・ Double consonant ・ Double Contact ・ Double contrabass flute ・ Double copula ・ Double coset ・ Double counting ・ Double counting (accounting) ・ Double counting (fallacy) ・ Double counting (proof technique) ・ Double cover ・ Double coverage ・ Double Crater ・ Double criminality ・ Double Cross ・ Double Cross (1941 film) ・ Double Cross (1972 film) ・ Double Cross (2005 film) ・ Double Cross (album) ・ Double Cross (novel) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Double coset ： ウィキペディア英語版 Double coset In mathematics, given a group ''G'' and two subgroups ''H'' and ''K'', not necessarily distinct, a double coset (or more precisely an (''H'',''K'') double coset) is a set ''HgK'' for some fixed element ''g'' in ''G''. Equivalently, an (''H'',''K'') double coset in ''G'' is an equivalence class for the equivalence relation defined on ''G'' by :''x'' ~ ''y'' if there are ''h'' in ''H'' and ''k'' in ''K'' with ''hxk'' = ''y''. The basic properties of double cosets follow immediately from the fact that they are equivalence classes; namely, two double cosets ''HxK'' and ''HyK'' are either disjoint or identical and ''G'' is partitioned into its (''H'',''K'') double cosets. Furthermore, each double coset ''HgK'' is a union of ordinary right cosets ''Hy'' of ''H'' in ''G'' and left cosets ''zK'' of ''K'' in ''G''. In particular, the number of right cosets of ''H'' in ''HgK'' is the index (∩ ''g''-1''Hg'' ) and the number of left cosets of ''K'' in ''HgK'' is the index (∩ ''g''-1''Hg'' ).〔 Double cosets are in fact orbits for the group action of ''H''×''K'' on ''G'' with $(h,k).g\; :=\; hgk^$. The set of double cosets is often denoted by :$H\; \backslash backslash\; G\; /\; K.$ == Algebraic structure == It is possible to define a product operation of double cosets in an associated ring. Given two double cosets $H\; g\_1\; K$ and $K\; g\_2\; L$, we decompose each into right cosets $\backslash textstyle\; H\; g\_1\; K\; =\; \backslash coprod\_i\; H\; a\_i$ and $\backslash textstyle\; K\; g\_2\; L\; =\; \backslash coprod\_j\; b\_j\; L$. If we write $c\_g\; =\; \backslash left\; |\; \backslash \; \backslash right\; |$, then we can define the product of $H\; g\_1\; K$ with $K\; g\_2\; L$ as the formal sum $\backslash textstyle\; H\; g\_1\; K\; \backslash cdot\; K\; g\_2\; L\; =\; \backslash sum\_\; c\_g\; H\; g\; L$. An important case is when ''H'' = ''K'' = ''L'', which allows us to define an algebra structure on the associated ring spanned by linear combinations of double cosets. 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「Double coset」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.