Paul
Posts:
676
Registered:
7/12/10


Re: Free group on m generators elementary extension of the free group on n generators (n < m)?
Posted:
Jul 14, 2013 6:15 AM


On Sunday, July 14, 2013 10:52:20 AM UTC+1, Sandy wrote: > pepstein5@gmail.com 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 nonabelian group has an abelian subgroup, this is a nonelementary 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.
Am I more on target now?
Thanks.
Paul

