Finite Subgroup Test Let H be a non-empty nite subset of a group G. Then H is a subgroup of G if H is closed under the operation of G. Proof. In view of the Two Step Subgroup Test1 we need only:I prove that [1'1 E H whenever a E H. If e = s, then 421 = a and we are done. If a 5-2 e, consider the sequence o, o\