# Alg7.6

From Example Problems

Prove that and , if and only if is a subgroup of .

If is a subgroup of , by the properties of identity, closure and inverse, it is true that and .

If , show that this implies is a subgroup of .

__Identity__: First let so that .

__Inverse__: Let so that .

__Closure__: Let so that .

__Associativity__: If , then which is not true by the assumption that is a group.