“ProofThatAllCyclicGroupsAreAbelian”的概念、定义、习题解题方法及翻译-数学辞典

单词	ProofThatAllCyclicGroupsAreAbelian
释义	proof that all cyclic groups are abelian The following is a proof that all cyclic groups are abelian. Proof. Let $G$ be a cyclic group and $g$ be a generator of $G$ . Let $a,b\\in G$ . Then there exist $x,y\\in{\\mathbb{Z}}$ such that $a=g^{x}$ and $b=g^{y}$ . Since $ab=g^{x}g^{y}=g^{x+y}=g^{y+x}=g^{y}g^{x}=ba$ , it follows that $G$ is abelian.∎
随便看	ExtremePoint extreme point ExtremeSubsetOfConvexSet extreme subset of convex set ExtremeValueTheorem extreme value theorem Extremum extremum ExtremumPointsOfFunctionOfSeveralVariables extremum points of function of several variables FaaDiBrunosFormula FaceOfAConvexSet face of a convex set FaceOfAConvexSetAlternativeDefinitionOf face of a convex set, alternative definition of FactorEmbeddable factor embeddable Factorial factorial FactorialBase factorial base FactorialBaseRepresentationOfFractions factorial base representation of fractions FactorialModuloPrimePowers factorial modulo prime powers

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

proof that all cyclic groups are abelian