Timeline for Are there algorithms and/or criteria for determining if a group has a presentation with all commutator relators?

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Sep 18, 2013 at 8:23	comment	added	HJRW		Here's another necessary condition: if your group $G$ is not free, then $b_2(G)>0$. Stallings proved (Homology and central series of groups, J. Algebra) that, in a group with $H_2(G,\mathbb{Q})=0$, any linearly independent subset in $H_1$ generates a free subgroup. But the generating set in your presentation is linearly independent in $H_1$.
Sep 17, 2013 at 17:00	history	edited	Nick Salter	CC BY-SA 3.0	added 47 characters in body
Sep 17, 2013 at 16:58	comment	added	Nick Salter		Yes, I mean a product of commutators. I'll edit the language to make it more precise.
Sep 17, 2013 at 15:49	comment	added	HJRW		To be clear, for you, a 'commutator relation' is a relation which is a product of commutators, right?
Sep 17, 2013 at 15:31	comment	added	Nick Salter		Ah - that's a good point. I've edited my question.
Sep 17, 2013 at 15:30	history	edited	Nick Salter	CC BY-SA 3.0	added 226 characters in body
Sep 17, 2013 at 15:23	comment	added	Andy Putman		This is impossible. The trivial group is the only group with this property whose abelianization is trivial, so if you could solve this problem then you could decide whether a group presentation gave the trivial group.
Sep 17, 2013 at 15:18	history	asked	Nick Salter	CC BY-SA 3.0