翻訳と辞書 Words near each other ・ Torside Reservoir ・ Torsin A ・ Torsion ・ Torsion (algebra) ・ Torsion (gastropod) ・ Torsion (mechanics) ・ Torsion abelian group ・ Torsion bar suspension ・ Torsion box ・ Torsion coefficient (topology) ・ Torsion conjecture ・ Torsion constant ・ Torsion dystonia ・ Torsion field ・ Torsion field (pseudoscience) ・ Torsion group ・ Torsion of a curve ・ Torsion pendulum clock ・ Torsion sheaf ・ Torsion siege engine ・ Torsion spring ・ Torsion subgroup ・ Torsion tensor ・ Torsion-Bar Antenna ・ Torsion-free ・ Torsion-free abelian group ・ Torsion-free abelian groups of rank 1 ・ Torsion-free module ・ Torsional strain ・ Torsional vibration 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 Torsion group ： ウィキペディア英語版 Torsion group In group theory, a branch of mathematics, a torsion group or a periodic group is a group in which each element has finite order. All finite groups are periodic. The concept of a periodic group should not be confused with that of a cyclic group. The exponent of a periodic group ''G'' is the least common multiple, if it exists, of the orders of the elements of ''G''. Any finite group has an exponent: it is a divisor of |''G''|. Burnside's problem is a classical question, which deals with the relationship between periodic groups and finite groups, if we assume only that ''G'' is a finitely-generated group. The question is whether specifying an exponent forces finiteness (to which the answer is 'no', in general). Examples of infinite periodic groups include the additive group of the ring of polynomials over a finite field, and the quotient group of the rationals by the integers, as well as their direct summands, the Prüfer groups. Another example is the union of all dihedral groups. None of these examples has a finite generating set, and any periodic linear group with a finite generating set is finite. Explicit examples of finitely generated infinite periodic groups were constructed by Golod, based on joint work with Shafarevich, see Golod–Shafarevich theorem, and by Aleshin and Grigorchuk using automata. ==Mathematical logic== One of the interesting properties of periodic groups is that they cannot be formalized in terms of first-order logic. This is because doing so would require an axiom of the form :$\backslash forall\; x.\backslash ,\; ((x=e)\; \backslash lor\; (x\backslash circ\; x=e)\; \backslash lor\; ((x\backslash circ\; x)\backslash circ\; x=e)\; \backslash lor\; \backslash cdots)$ which contains an infinite disjunction and is therefore inadmissible. It is not possible to get around this infinite disjunction by using an infinite set of axioms: the compactness theorem implies that no set of first-order formulae can characterize the torsion groups. 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「Torsion 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.