Students will learn the definition of a subgroup, as seen here, and practice proving different things are, or are not, subgroups. For example, prove \(H = 2\mathbb{Z}\) is a subgroup of \(\mathbb{Z}\). The solution is here. After that, they'll learn why the intersection of two subgroups is also a subgroup. That proof can be found here. Finally, they'll see a generalization of this result, which proves the intersection of a nonempty set of subgroups is a subgroup. That proof is here.
