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State/Intersections of subgroups are subgroups
Proposition: (The intersection of subgroups is a subgroup.) Suppose that $G$ is a group. Suppose that $M$ is a set of subgroups of $G$, i.e., if $m \in M$ then $m$ is a subgroup of $G$. Then the intersection $\bigcap M$ is a subroup of $G$.
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