^ From:

> ^ Subject:

Dear gap-forum

I would like to look at the second homology

of SL(2,A) where A is a ring of S-integers.

The example of interest is A=Z[u,1/5] with u

a primitive 5-th root of unity (Z is the ring

of rational integers).

One way to look at the second homology is to

take a finite presentation R-->F-->SL(2,A)

in which F is free and R is the normal closure

of a set of relators. (So I believe that it

is possible to have a finite set of generators

and o finite set of relators). Then I can use

the Hopf formula for the second homology group

H = R&[F,F]/[R,F]

where "&" means intersection.

Here there are a couple of questions (I don't know

gap and I try to make sense of the manual).

1. Suppose I know a finite set of matrices generating

SL(2,A). How can I find the relators?

2. Suppose I know the generators and the relators.

What

strategy I need to calculate the group H above?

3. Is it any other better way to calculate H using

gap? (via cell-complexes for instance)

Sorry for the trouble, but I really need to see an

example.

Comment: I will be also happy if for a given prime p

I can show that the p-torsion of H is zero.

Best regards,

M Anton

__________________________________________________ Do You Yahoo!? Get email at your own domain with Yahoo! Mail. http://personal.mail.yahoo.com/?.refer=text

> < [top]