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单词 Split extension
释义

Split extension

原声例句
摩登家庭第八季_Modern Family-Season08

Watch their faces when I tell them we could kewpie a scorpion into a cradle catch and then pop up into a split extension.

炫耀一下我们能以蝎子倒立姿势，抛起再接住，然后马上叠罗汉，同时看看她们叹服的表情。

中文百科

群扩张 Group extension

（重定向自Split extension）

在抽象代数中，设 Q 为群，若存在群 G, N，及群的正合串行

1 \to N \stackrel{i}{\to} G \stackrel{p}{\to} Q \to 1

（换言之，i 是单射、p 是满射，且 \mathrm{Ker}(p)=\mathrm{Im}(i)；是故可视 N 为 G 的正规子群， G/N \simeq Q。）则称群 G 为 Q 的群扩张，或称 Q 对 N 的扩张。

由短正合串行的同构关系，可以定义群扩张的等价类。若某个群扩张等价于

1 \to N \to N \times Q \to Q \to 1

则称此扩张为平凡扩张。当 N 落在 G 的中心时，称之为中心扩张。

英语百科

Group extension 群扩张

（重定向自Split extension）
Figure 1

In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence

If G is an extension of Q by N, then G is a group, N is a normal subgroup of G and the quotient group G/N is isomorphic to the group Q. Group extensions arise in the context of the extension problem, where the groups Q and N are known and the properties of G are to be determined. Note that the phrasing "G is an extension of N by Q" is also used by some.
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更新时间：2025/6/21 19:02:48