Group action(the action of a group on a set, 群在集合上的作用) 是任何一本像样的群论入门书都会讲到的概念. 这概念是如此的重要, 在几何, 拓扑, 分析, 数论中用处广泛, 更不论代数了.

Let $$G$$ be a group and let $$X$$ be a set. Let $$S(X)$$ be the group of all permutations of $$X$$. An action or an operation of $$G$$ on $$X$$ is a homomorphism

$\pi\colon G\to S(X)$

of $$G$$ into $$S(X)$$.

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