On Sunday, July 14, 2013 10:52:20 AM UTC+1, Sandy wrote: > firstname.lastname@example.org wrote: > > > > > If I'm not confused[...] > > > > But you are! Btw, my other post that I referred to just a few minutes > > ago in reply to Butch, is in sci.logic as a reply to Rupert. > > > > I have added in sci.logic for this reply.
I think I get it now. When a non-abelian group has an abelian subgroup, this is a non-elementary extension because the statement "For all x, For all y, xy = yx" is false in the larger group but true in the subgroup.
I think the question with which you opened the post is basically equivalent to asking whether the theorem cited by David is correct.