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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 Binary cyclic group ： ウィキペディア英語版 Binary cyclic group In mathematics, the binary cyclic group of the ''n''-gon is the cyclic group of order 2''n'', $C\_$, thought of as an extension of the cyclic group $C\_n$ by a cyclic group of order 2. It is the binary polyhedral group corresponding to the cyclic group.〔.〕 In terms of binary polyhedral groups, the binary cyclic group is the preimage of the cyclic group of rotations () under the 2:1 covering homomorphism :$\backslash operatorname(3)\; \backslash to\; \backslash operatorname(3)\backslash ,$ of the special orthogonal group by the spin group. As a subgroup of the spin group, the binary cyclic group can be described concretely as a discrete subgroup of the unit quaternions, under the isomorphism $\backslash operatorname(3)\; \backslash cong\; \backslash operatorname(1)$ where Sp(1) is the multiplicative group of unit quaternions. (For a description of this homomorphism see the article on quaternions and spatial rotations.) ==See also== *binary dihedral group *binary tetrahedral group *binary octahedral group *binary icosahedral 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「Binary cyclic 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.