Re: Subgroups of a group

On Mar 25, 8:01 pm, "searcher" <x32582...@xxxxxxxxx> wrote:
Can anyone answer the following for me?

If G is a group (not necessarily finite) and A, B are subgroups of G
such that G = AB union BA, must G = AB = BA?

It's true if G is finite, but I guess you already knew that. If there
is a counterexample where G is infinite, then G is the union of two
proper subsemigroups, namely {g: gA subset AB} and {g: Ag subset BA}.
Can an infinite group be the union of two proper subsemigroups?

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