# Definition(s)
> [!NOTE] Definition 1 (Conjugate)
> Let $G$ be a [[Groups|group]] and $H$ a [[Subgroup|subgroup]] of $G.$
> A conjugate of $H$ is the set of the form $gHg^{-1}=\{ ghg^{-1} \mid h\in H \}$for some $g\in G.$
> [!Example] Example
> Contents
# Properties(s)
# Application(s)
A subgroup is [[Normal Subgroup|normal]] iff all its conjugates satisfy $gHg^{-1}=H.$
# Bibliography