



 
Hi, Suppose P and Q are both normal subgroups of G and let $R = P \cap Q.$ Let $x \epsilon G$ then you need to show that $R = x^{1}Rx.$ Let $y \; \epsilon x^{1}Rx$ they $y = x^{1}rx$ for some $r \epsilon R.$ But since $R = P \cap Q,$ $r$ is an element of $P$ and $Q$ and hence, since $P$ and $Q$ are normal subgroups, $x^{1}rx \epsilon P \cap Q = R.$ Thus $y \epsilon R$ and hence $x^{1}Rx \subset R.$ Now let $s \epsilon R, x \epsilon G$ and show that $s \epsilon x^{1}Rx.$ Penny  


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