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单词 Inner automorphism
释义

Inner automorphism

英语例句库

Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.

【摘要】: 正 It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other.

中文百科

内自同构

在抽象代数的群论中,内自同构是群的自同构的一种。设g为群G的一个元素,则g对应的内自同构,是以g的共轭作用定义如下

G的一个自同构,如果是G的元素的共轭作用,便称为内自同构

gG的中心Z(G)内,则\iota_g是平凡的。因此阿贝尔群的内自同构都是平凡的。一般而言,\iota_g的不动点集,正是g的中心化子CG(g)。

内自同构\iota_g的逆元是\iota_g^{-1}=\iota_{g^{-1}}。两个内自同构\iota_g, \iota_h的复合是\iota_g\circ \iota_h=\iota_{gh}

由群的中心的基本性质可知,若Inn(G)是循环群,则Inn(G)是平凡群。

若Inn(G)=Aut(G)且G无中心,则G称为完备群。

G是完满群且Inn(G)是单群,则G称为拟单群。

英语百科

Inner automorphism 内自同构

In abstract algebra an inner automorphism is a function in which an initial operation is applied, then another operation, and then the initial operation is reversed. With letters to indicate the operations and thing-being-transformed: fgf(X). Sometimes the initial action and its subsequent reversal change the overall result ("raise umbrella, walk through rain, lower umbrella" has a different result from just "walk through rain"), and sometimes they do not ("take off left glove, take off right glove, put on left glove" has the same effect as only "take off right glove").

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