翻訳と辞書 Words near each other ・ Lampione ・ Lampiri ・ Lampitt Nunatak ・ Lampius ・ Lampião ・ Lampkin ・ Lampkowo ・ Lamplaimat Pattana School ・ Lampland ・ Lampland (lunar crater) ・ Lampland (Martian crater) ・ Lampleigh v Brathwait ・ Lamplight ・ Lamplighter ・ Lamplighter (disambiguation) ・ Lamplighter group ・ Lamplighter Stakes ・ Lamplighter's Serenade ・ Lamplighters Marsh ・ Lamplighters Music Theatre ・ Lamplighters Theatre ・ Lamplighters Yeshivah ・ Lamplough Wallgate ・ Lamplough, Victoria ・ Lamplugh ・ Lamplugh (surname) ・ Lamplugh Glacier ・ Lamplugh Inlet ・ Lamplugh Island ・ Lamplughsaura 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 Lamplighter group ： ウィキペディア英語版 Lamplighter group In mathematics, the lamplighter group ''L'' of group theory is the restricted wreath product Z/2Z ≀ Z. The base group ''B'' of ''L'' is :$\backslash bigoplus\_^\backslash infty\; \backslash mathbb/2\backslash mathbb,$ and so ''L''/''B'' is isomorphic to Z. The standard presentation for the lamplighter group arises from the wreath product structure :$\backslash langle\; a,\; t\; \backslash mid\; a^2,\; (t^m\; a\; t^\; ,\; t^n\; a\; t^),\; m,\; n\; \backslash in\; \backslash mathbb\; \backslash rangle$, which may be simplified to :$\backslash langle\; a,\; t\; \backslash mid\; (a\; t^n\; a\; t^)^2,\; n\; \backslash in\; \backslash mathbb\; \backslash rangle$. The generators ''a'' and ''t'' are intrinsic to the group's notable growth rate, though they are sometimes replaced with ''a'' and ''at'', changing the logarithm of the growth rate by at most a factor of 2. The name of the group comes from viewing the group as acting on a doubly infinite sequence of street lamps ..., ''l''-2, ''l''-1, ''l''0, ''l''1, ''l''2, ..., each of which may be on or off, and a lamplighter standing at some lamp ''l''''k''. The generator ''t''  increments ''k'', so that the lamplighter moves to the next lamp (''t'' -1 decrements ''k''), while the generator ''a'' means that the state of lamp ''l''''k'' is changed (from off to on or from on to off). We may assume that only finitely many lamps are lit at any time, since the action of any element of ''L'' changes at most finitely many lamps. The number of lamps lit is, however, unbounded. The group action is thus similar to the action of a Turing machine. ==See also== * Growth rate (group theory) 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「Lamplighter 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.