翻訳と辞書 Words near each other ・ Bounded growth ・ Bounded inverse theorem ・ Bounded mean oscillation ・ Bounded operator ・ Bounded pointer ・ Bounded quantification ・ Bounded quantifier ・ Bounded rationality ・ Bounded Retransmission Protocol ・ Bounded set ・ Bounded set (topological vector space) ・ Bounded Type ・ Bounded type (mathematics) ・ Bounded variation ・ Bounded weak echo region ・ Boundedly generated group ・ Boundedness ・ Boundedness (linguistics) ・ Bounden (video game) ・ Bounder ・ Bounder (video game) ・ Boundiale ・ Boundiali ・ Boundiali Airport ・ Boundiali Department ・ Boundido ・ Boundin' ・ Bounding Home ・ Bounding interval hierarchy ・ Bounding Main 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 Boundedly generated group ： ウィキペディア英語版 Boundedly generated group In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see ). == Definitions == A group ''G'' is called ''boundedly generated'' if there exists a finite subset ''S'' of ''G'' and a positive integer ''m'' such that every element ''g'' of ''G'' can be represented as a product of at most ''m'' powers of the elements of ''S'': : $g\; =\; s\_1^\; \backslash cdots\; s\_m^,$ where $s\_i\; \backslash in\; S$ and $k\_i$ are integers. The finite set ''S'' generates ''G'', so a boundedly generated group is finitely generated. An equivalent definition can be given in terms of cyclic subgroups. A group ''G'' is called ''boundedly generated'' if there is a finite family ''C''1, …, ''C''''M'' of not necessarily distinct cyclic subgroups such that ''G'' = ''C''1…''C''''M'' as a set. 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「Boundedly generated 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.