(related to Theorem: Order of Subgroup Divides Order of Finite Group)

- By hypothesis, \((G,\ast)\) is a group with a finite order \(|G| < \infty\) and \(H\subseteq G\) is its subgroup.
- All left cosets of $G$ are disjoint and $G$ is the set union of them.
- Since the subgroups and their cosets are equipotent, their order is $|H|$ and there are exactly $|G/H|$ of them.∎

**Modler, Florian; Kreh, Martin**: "Tutorium Algebra", Springer Spektrum, 2013