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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 $G$.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Subgroup, Def/Intersection

The following statements and definitions rely on the material of this page: Def/Generate (group)

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