翻訳と辞書 Words near each other ・ Finite volume method for one-dimensional steady state diffusion ・ Finite volume method for three-dimensional diffusion problem ・ Finite volume method for two dimensional diffusion problem ・ Finite volume method for unsteady flow ・ Finite water-content vadose zone flow method ・ Finite wing ・ Finite-difference frequency-domain method ・ Finite-difference time-domain method ・ Finite-dimensional distribution ・ Finite-dimensional von Neumann algebra ・ Finite-rank operator ・ Finite-state machine ・ Finitely generated ・ Finitely generated abelian group ・ Finitely generated algebra ・ Finitely generated group ・ Finitely generated module ・ Finitely generated object ・ Finitely presented ・ Finiteness theorem ・ Finitism ・ Finito ・ Finitribe ・ Finity's End ・ Finix Comics ・ Finiș ・ Finiș River ・ Finișel River ・ Finja ・ Finjan 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 Finitely generated group ： ウィキペディア英語版 Finitely generated group In algebra, a finitely generated group is a group ''G'' that has some finite generating set ''S'' so that every element of ''G'' can be written as the product of finitely many elements of the finite set ''S'' and of inverses of such elements. Every finite group is finitely generated, since ''S'' can be taken to be ''G'' itself. Every infinite finitely generated group must be countable. A group that is generated by a single element is called cyclic. Every infinite cyclic group is isomorphic to the additive group of the integers Z. The additive group of rational numbers Q, while countable, is not finitely generated. ==Quotients and subgroups== Every quotient of a finitely generated group is finitely generated. However, a subgroup of a finitely generated group need not be finitely generated. For example, the commutator subgroup of the free group ''F''2 on two generators is not finitely generated. However, a subgroup of finite index in a finitely generated group is always finitely generated, and the Schreier index formula gives a bound on the number of generators required.〔Rose 2012, p. 55〕 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「Finitely 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.