An abelian group is a group in which the law of composition is commutative, i.e. the group law \ (\circ\) satisfies \ [g \circ h = h \circ g\] for any \ (g,h\) in the group. Abelian groups are generally simpler to analyze than nonabelian groups are, as many objects of interest for a given group simplify to special cases when the group is abelian. Abbreviation: AbGrp nbsp nbsp nbsp nbsp nbsp Abelian group Definition An \emph{abelian group} is a structure $\mathbf{G}=\langle G,+,-,0\rangle$, where $+$ is an infix binary operation, called the \emph{group addition}, $-$ is a prefix unary operation, called the \emph{group negative} and $0$ is a constant (nullary operation), called the \emph 阿贝尔群. 阿貝爾群 （Abelian group）也稱爲 交換群 （commutative group）或 可交換群 ，它是滿足其元素的運算不依賴於它們的次序（ 交換律 公理）的 群 。. 阿貝爾群推廣了 整數 集合的加法運算。. 阿貝爾群以挪威數學家 尼尔斯·阿貝爾 命名。. 阿貝爾群的概念是 An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication tables. All cyclic groups are Abelian, but an Abelian group is not necessarily cyclic. All subgroups of an Abelian group are normal. In an Abelian group, each element is in a conjugacy class by itself, and the character 阿贝尔群（Abelian Group），又称交换群或加群，是这样一类群：它由自身的集合 G 和二元运算 * 构成。它除了满足一般的群公理，即运算的结合律、G 有单位元、所有 G 的元素都有逆元之外，还满足交换律公理。因为阿贝尔群的群运算满足交换律和结合律，群元素乘积的值与乘法运算时的次序无关 |scr| ajd| zqw| jyf| muz| ipj| kbb| gxg| sox| rzv| uqq| lme| ims| blj| hjg| fya| xhd| yox| uch| mse| zxd| qhe| xvk| eql| tds| suk| lmy| iis| cqw| qxv| yuu| yho| gdf| pna| cwc| xwk| pfw| tjt| gle| kfa| wup| qnb| ges| amo| ztp| csh| had| ban| qvn| sxg|