1. The problem statement, all variables and given/known data Let G be a finite group andd H a subset of G. Prove H is a subgroup of G iff H is closed. 2. Relevant equations 3. The attempt at a solution Let G be a finite group and H be a subgroup. G is a finite group, therefore it is closed, has an inverse and has an identity. We want to show H is only a subgroup of G iff H is closed. To be a subgroup, H must be closed, contain the identity element of G, and contain the inverse. Now I'm stuck.