Bill Allombert on Mon, 03 Apr 2017 15:26:55 +0200

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Re: Reuse of data in rnfkummer/computing order of galois elements without it

On Mon, Apr 03, 2017 at 05:13:31AM -0700, Watson Ladd wrote:
> Order as in group theory.
> Let K/Q a galois extension, and f a conductor of K that is invariant
> by Gal(K/Q).
> bnrgaloismatrix gives the action of Gal(K/Q) on Cl_f(K).
> bnrisgalois() allows to find the subgroups of Cl_f(K) that gives rise to
> Galois extension of Q.
> Well, I've already got them: I'm taking a compositum of quadratic
> extensions L of a field K which will be Galois. I want to throw out L where
> Gal(L/Q) has an element that is too large.

I think the question is related to whether there is a subfield K' of K
such that L/K' is Abelian.