Timeline for Generators of sections of free groups

5 events

when toggle format	what		by	license	comment
May 12, 2013 at 14:30	vote	accept	Yassine Guerboussa
May 10, 2013 at 16:43	comment	added	Andy Putman		It's nontrivial to compute it, but there is a huge literature on group cohomology, so there are many tools available. To help your search, you should be aware that $H_2(G;\mathbb{Z})$ is also known as the Schur multiplier of $G$. For a particular finite group of reasonable size, by the way, you should be able to compute $H_2$ using GAP. The relevant packages are cohomolo (see gap-system.org/Packages/cohomolo.html) and hap (see gap-system.org/Packages/hap.html).
May 10, 2013 at 11:00	comment	added	Yassine Guerboussa		also it is not difficult to prove that $F/[F,F]F^p$ is elementary abelian of rank d, and so is $H_1(F,Z/p)$. It follows from your last exact sequence that $H/[F,H]H^p$ and $H_2(Q,Z/p)$ are isomorphic. So we have only to compute $H_2(Q,Z/p)$. I may ask how much harder to do this?
May 10, 2013 at 10:53	comment	added	Yassine Guerboussa		Thank you dear professor andy Putman. clearly we can start by a minimally d-generated group Q (I'm interested to the case when Q is a finite p-group), in that case $H_1(Q,Z/p) is isomorphic to the frattini quotient of Q, so it is elementary abelian of rank d.
May 9, 2013 at 16:54	history	answered	Andy Putman	CC BY-SA 3.0