Exterior square of finite group is finite

From Groupprops
Jump to: navigation, search


Suppose G is a finite group. Then, the exterior square of G is also a finite group.


Facts used

  1. Commutator map is homomorphism from exterior square to derived subgroup, and the kernel of this homomorphism is the Schur multiplier.
  2. Schur multiplier of finite group is finite


The proof basically follows directly by combining Facts (1) and (2).