Subgroup Question
Let $G$ be a group and let $A \subset G$. I want to show that there is a
$\subset$-least subgroup $H$ of $G$ such that $A \subset H$. The subgroup
is noted as $<A>$.
Then I want to show that $<A>$ is the set of all finite products of the
elements of $A$.
Kinda confused on how to start this one. I know that $<A>$ us a subgroup
of $G$, so it is closed under multiplication and inverses and also
contains $A$. Therefore, $<A>$ must contain the products that are in $H$?
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