Let $G$ a group and $X$ a subset of $G$. Let $X^G=\langle X^a : a \in G\rangle$, where $X^a=aXa^{-1}$. Show (using the conjugation classes theory) that $G$ is a minimal normal subroup of $G$ containing $X$.
Using conjugation classes
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abstract-algebra
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0Do you mean to show that $X^G$ is a minimal normal subgroup of $G$ containing $X$? – 2012-10-16