While dealing with a question on the forum, I came up with the following problem:
If is a subgroup of a group , and , does imply ? In other words, is it possible to have ?
The answer (to the last question) is "no" if is finite. Or if is a normal subgroup. But what else?
I think this is either easy or false, but I can find neither a proof nor a counterexample...
I hope some people can help,
Thanks in advance,