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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 Tarski monster ： ウィキペディア英語版 Tarski monster group In the area of modern algebra known as group theory, a Tarski monster group, named for Alfred Tarski, is an infinite group ''G'', such that every proper subgroup ''H'' of ''G'', other than the identity subgroup, is a cyclic group of order a fixed prime number ''p''. A Tarski monster group is necessarily simple. It was shown by A. Yu. Olshanskii in 1979 that Tarski groups exist, and that there is a Tarski ''p''-group for every prime ''p'' > 1075. They are a source of counterexamples to conjectures in group theory, most importantly to Burnside's problem and the von Neumann conjecture. ==Definition== Let $p$ be a fixed prime number. An infinite group $G$ is called a Tarski Monster group for $p$ if every nontrivial subgroup (i.e. every subgroup other than 1 and G itself) has $p$ elements. 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「Tarski monster 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.