“PerfectGroup”的概念、定义、习题解题方法及翻译-数学辞典

单词	PerfectGroup
释义	perfect group A group $G$ is called perfect if $G=[G,G]$ , where $[G,G]$ is the derived subgroup of $G$ , or equivalently, if the abelianization of $G$ is trivial.
随便看	Identity types Identity types and identity systems idèle IfAAndBCommuteSoDoAAndB1 If A and B commute so do A and B^{-1} IfAinMnRAndAIsSupertriangularThenAn0 IfAIsConvexAndFLinearThenFAAndF1AAreConvex if A is convex and f linear then f⁢(A) and f^{-1}⁢(A) are convex IfAIsInfiniteAndBIsAFiniteSubsetOfAThenAsetminusBIsInfinite if A is infinite and B is a finite subset of A⁢ERROR(\tmspace)+.1667⁢e⁢m⁢ERROR(\tmspace)-.1667⁢e⁢m, then A∖B is infinite IfAnIsIrrationalThenaIsIrrational if a^n is irrational then a is irrational If A∈M_n⁢(R) and A is supertriangular then A^n=0 IfDxiXi112iThenXiIsACauchySequence if d⁢(x_i,x_{i+1})<1/2^i then x_i is a Cauchy sequence IfFcolonXtoYIsContinuousThenFcolonXtoFXIsContinuous If f⁢m⁢MERROR(onscript):X→Y is continuous then f⁢m⁢MERROR(onscript):X→f⁢(X) is continuous IFlogic IF-logic Ifmun1omeganThentaun2omegan Ifsumk1inftyAkConvergesThenAkto0 IfTheAlgebraOfFunctionsOnAManifoldIsAPoissonRingThenTheManifoldIsSymplectic if the algebra of functions on a manifold is a Poisson ring then the manifold is symplectic if μ⁢(n)=(-1)^{ω⁢(n)} then τ⁢(n)=2^{ω⁢(n)} if ∑@⁢ERROR(\slimits)⁢@⁢@⁢@_{k=1}^∞⁢a_k converges then a_k→0

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。

perfect group