Talk:Subgroup test

Would one ever use the one-step subgroup test?
I'm not convinced that this concept deserves its own article, instead of being part of the subgroup article (as they already are, without the proof).

Also, are there actual situations in the literature where it is easier to check that $$ab^{-1} \in H$$ for all $$a,b \in H$$ than it is to test the more natural conditions of being closed under multiplication and taking inverses? The one-step test feels like a kludge. Ebony Jackson (talk) 23:22, 31 December 2020 (UTC)