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本帖最后由 hbghlyj 于 2023-4-14 23:40 编辑 Groups and Geometry, 2007
Example 10.7:
Suppose that $G$ is a group acting on a non-empty set $X$ and we write
$$H = \{g ∈ G : gx = x\text{ for all }x ∈ X\}$$
Then $H$ is a normal subgroup of $G$ and, if we take
$$(gH)x = gx,$$
then $G/H$ acts faithfully on $X$. |
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