Prove that if H and K are normal subgroups of a group G then their intersection H ∩ K is also a normal subgroup of G.
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A subgroup \(N\) of a group \(G\) is normal if for every element \(g \in G\) and every element \(n \in N\), the element \(gng^{-1}\) is also in \(N\). This property ensures that the left and right cosets of \(N\) in \(G\) are the same. Show more…
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If $H$ and $K$ are subgroups of a group $G$, prove that $H \cap K$ is a subgroup of $G$. (Remember that $x \in H \cap K \quad$ iff $\quad x \in H \quad$ and $\quad x \in K)$.
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