Infimum of Subgroups in Lattice

Theorem
Let $\left({G, \circ}\right)$ be a group.

Let $\mathbb G$ be the set of all subgroups of $G$.

Let $\left({\mathbb G, \subseteq}\right)$ be the complete lattice formed by $\mathbb G$ and $\subseteq$.

Let $H, K \in \mathbb G$.

Then:
 * $\inf \left\{{H, K}\right\} = H \cap K$

Proof
Let $H, K \in \mathbb G$.

From Set of Subgroups forms Complete Lattice:


 * $\inf \left\{{H, K}\right\} = H \cap K$