Math and science::Algebra::Aluffi

# Groups. Lagrange's theorem.

### Lagrange's theorem

Let $$G$$ be a group, and let $$H \subset G$$ be a subgroup. Then:

[$|G| = \quad ?$]

There are three corollaries on the reverse. Can you remember them?

1. About the order of $$g$$ in $$G$$.
2. When $$|G|$$ is a prime.
3. Fermat's little theorem.