Exterior square of finite group is finite
- Schur-Baer theorem: This states that if the inner automorphism group of a group is finite, so is the derived subgroup of the group.
- Commutator map is homomorphism from exterior square to derived subgroup, and the kernel of this homomorphism is the Schur multiplier.
- Schur multiplier of finite group is finite
The proof basically follows directly by combining Facts (1) and (2).