I want to know the answer to the following question:
What essential condition must be met for a subset of a group to be a subgroup?
All the background I'm provided with is that "The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g−1h ∈ H for all elements g, h ∈ H. Knowing the subgroups is important in understanding the group as a whole.d[›]". Is that enough to answer the question?
Answer: yes