Question
Let $C^{\prime}=\left\{a \in G:(a x)^{2}=(x a)^{2}\right.$ for every $\left.x \in G\right\}$. Prove that $C^{\prime}$ is a subgroup of $G$.Let $C^{\prime}=\left\{a \in G:(a x)^{2}=(x a)^{2}\right.$ for every $\left.x \in G\right\}$. Prove that $C^{\prime}$ is a subgroup of $G$.
Step 1
For any $x \in G$, we have $(abx)^2 = a(bx)^2a = a(xb)^2a = (axb)^2 = (xba)^2 = x(ba)^2 = (xba)^2 = (xab)^2$. Hence, $ab \in C'$. Show more…
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