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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 Locally profinite group ： ウィキペディア英語版 Locally profinite group In mathematics, a locally profinite group is a hausdorff topological group in which every neighborhood of the identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is hausdorff locally compact and totally disconnected. Moreover, a locally profinite group is compact if and only if it is profinite; this explains the terminology. Basic examples of locally profinite groups are discrete groups and ''p''-adic Lie group. Non-examples are real Lie groups which have no small subgroup property. In a locally profinite group, a closed subgroup is locally profinite, and every compact subgroup is contained in an open compact subgroup. == Examples == Important examples of locally profinite groups come from algebraic number theory. Let ''F'' be a non-archimedean local field. Then both ''F'' and $F^\backslash times$ are locally profinite. More generally, the matrix ring $\backslash operatorname\_n(F)$ and the general linear group $\backslash operatorname\_n(F)$ are locally profinite. Another example of a locally profinite group is the absolute Weil group of a non-archimedean local field: this is in contrast to the fact that the absolute Galois group of such is profinite (in particular compact). 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「Locally profinite 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.