I was just wondering if the product ab is in a subgroup, are a and b necessarily in the subgroup, as well?
The Attempt at a Solution
I think they are, but how would you prove that? Or is that obvious from closure under multiplication and you don't need to prove it? I know it works the "normal" way, that is if a and b are in the subgroup (or group), then ab is in it, as well, but I'm not sure about the reverse direction.
Thanks in advance for any replies.