翻訳と辞書 Words near each other ・ Dictyotrypeta ・ Dictys ・ Dictys Cretensis ・ Dictée/Liber Novus ・ Dicuil ・ Diculești ・ Dicus ・ Dicy ・ Dicy, West Virginia ・ Dicya ・ Dicyanamide ・ Dicyanoacetylene ・ Dicycla ・ Dicycla oo ・ Dicycle ・ Dicyclic group ・ Dicyclodes ・ Dicyclohexylamine ・ Dicyclohexylurea ・ Dicyclopentadiene ・ Dicycloplatin ・ Dicycloverine ・ Dicyema shimantoense ・ Dicyemida ・ Dicyemidae ・ Dicymbe ・ Dicymolomia ・ Dicymolomia diminutalis ・ Dicymolomia grisea ・ Dicymolomia julianalis 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 Dicyclic group ： ウィキペディア英語版 Dicyclic group In group theory, a dicyclic group (notation Dic''n'' or Q''4n'') is a member of a class of non-abelian groups of order 4''n'' (''n'' > 1). It is an extension of the cyclic group of order 2 by a cyclic group of order 2''n'', giving the name ''di-cyclic''. In the notation of exact sequences of groups, this extension can be expressed as: :$1\; \backslash to\; C\_\; \backslash to\; \backslash mbox\_n\; \backslash to\; C\_2\; \backslash to\; 1.\; \backslash ,$ More generally, given any finite abelian group with an order-2 element, one can define a dicyclic group. ==Definition== For each integer ''n'' > 1, the dicyclic group Dic''n'' can be defined as the subgroup of the unit quaternions generated by : x & = j \end More abstractly, one can define the dicyclic group Dic''n'' as any group having the presentation :$\backslash mbox\_n\; =\; \backslash langle\; a,x\; \backslash mid\; a^\; =\; 1,\backslash \; x^2\; =\; a^n,\backslash \; x^ax\; =\; a^\backslash rangle.\backslash ,\backslash !$ Some things to note which follow from this definition: * ''x''4 = 1 * ''x''2''a''''k'' = ''a''''k''+''n'' = ''a''''k''''x''2 * if ''j'' = ±1, then ''x''''j''''a''''k'' = ''a''−''k''''x''''j''. * ''a''''k''''x''−1 = ''a''''k''−''n''''a''''n''''x''−1 = ''a''''k''−''n''''x''2''x''−1 = ''a''''k''−''n''''x''. Thus, every element of Dic''n'' can be uniquely written as ''a''''k''''x''''j'', where 0 ≤ ''k'' < 2''n'' and ''j'' = 0 or 1. The multiplication rules are given by *$a^k\; a^m\; =\; a^$ *$a^k\; a^m\; x\; =\; a^x$ *$a^k\; x\; a^m\; =\; a^x$ *$a^k\; x\; a^m\; x\; =\; a^$ It follows that Dic''n'' has order 4''n''.〔 When ''n'' = 2, the dicyclic group is isomorphic to the quaternion group ''Q''. More generally, when ''n'' is a power of 2, the dicyclic group is isomorphic to the generalized quaternion group.〔 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「Dicyclic group」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.