Question
If $H$ is a subgroup of $G$, then by the centralizer $C(H)$ of $H$ we mean the set $\{x \in G \mid x h=h x$ for all $h \in H\} .$ Prove that $C(H)$ is a subgroup of $G$
Step 1
First, we need to show that the identity element of $G$ is in $C(H)$. Since $e_G h = h e_G = h$ for all $h \in H$, it follows that $e_G \in C(H)$. Show more…
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