conjugate

《代数学引论》 · 第 74 页

在共轭变换下，元素 $gxg^{-1}$ 称为与元素 $x$ 共轭；同样，子群 $gHg^{-1}$ 称为与子群 $H$ 共轭。

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《Algebra》 · 第 88-89 页 · Chapter II，Section 4「The Action of a Group on a Set」，Examples

Let $H$ be a subgroup of a group $G$. An action of $H$ on the set $G$ is given by $(h,x)\mapsto hxh^{-1}$; to avoid confusion with the product in $G$, this action of $h\in H$ is always denoted $hxh^{-1}$ and not $hx$. This action of $h\in H$ on $G$ is called conjugation by $h$ and the element $hxh^{-1}$ is said to be a conjugate of $x$.