Join and meet

Let $G=\mathbb{Z}/24$, $H=\langle 4\rangle$ and $K=\langle 6\rangle$. Then $H+K\simeq C_{12}$ and $H\cap K\simeq C_{2}$. Let us do this with Magma:

> R := ResidueClassRing(24);;
> G<g> := AdditiveGroup(R);
> H := sub<G|4*g>;
> K := sub<G|6*g>;
> GroupName(H+K);
C12
> GroupName(H meet K);
C2

We can indeed check that $H+K=\langle 2\rangle$ and $H\cap K=\langle 12\rangle$. In fact, both commands we see here

> H+K eq sub<G|2*g>;
true
> H meet K eq sub<G|12*g>;
true