Timeline for Must a group of defficiency > 1 be nonabelian?

8 events

when toggle format	what		by	license	comment
May 21, 2015 at 11:26	answer	added	YCor		timeline score: 6
May 21, 2015 at 10:54	history	edited	Pablo	CC BY-SA 3.0	added 43 characters in body
May 21, 2015 at 10:47	history	edited	Pablo	CC BY-SA 3.0	added 43 characters in body; edited tags
May 21, 2015 at 10:46	comment	added	Pablo		@AshotMinasyan I see thanks. I will edit the question to include the profinite case.
May 21, 2015 at 10:40	comment	added	Ashot Minasyan		A group is large if it has a finite index subgroup which maps onto the free group $F_2$ of rank $2$. Any large group contains a copy of $F_2$. You can read the proof of the theorem of Baumslag-Pride: it is very short. In the beginning they show that any group of deficiency at least 1 maps onto $\mathbb Z$; in particular, it is non-trivial.
May 21, 2015 at 10:36	comment	added	Pablo		@AshotMinasyan I am (sadly enough) not familiar with the terminology (what is a large group?). I would also like to know if the exists some (very elementary) argument showing that $F/S^F$ is nonabelian or merely nontrivial. I would be very glad if you could expand your comment to answer, clarifying these things for me.
May 21, 2015 at 10:27	comment	added	Ashot Minasyan		Of course: it is even large by a theorem of Baumslag-Pride [Baumslag, Benjamin; Pride, Stephen J. Groups with two more generators than relators. J. London Math. Soc. (2) 17 (1978), no. 3, 425–426]
May 21, 2015 at 10:14	history	asked	Pablo	CC BY-SA 3.0