Re: Galois action on class groups

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Mar 17, 2017 at 11:27:33AM +0000, LECOUTURIER Emmanuel wrote:
> Well, of course I assume that my question makes, sense, i.e. that K/Q
> is Galois and that one can view Gal(Q(zeta_p)/Q) as a subgroup of
> Gal(K/Q).

You mean a quotient of Gal(K/Q).
You can use bnrgaloismatrix for that.
Set
K=bnfinit(P);
G=galoisinit(K);
bnr=bnrinit(K,1,1);

Identify one element aut of G.group that map to the Frobenius.
(you can use galoissubgroups and galoisfixedfield for that).
and use
bnrgaloismatrix(bnr, aut) to get the matrix of the action
of aut on the class group.
then you should be able to use matsnf to find the group structure.

Cheers,
Bill.