Bill Allombert on Mon, 03 Apr 2017 12:23:56 +0200 |
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Re: Reuse of data in rnfkummer/computing order of galois elements without it |
On Sun, Apr 02, 2017 at 09:53:20PM -0700, Watson Ladd wrote: > 2: Is there a way to determine the maximal order of an element of the > Galois group of the resulting field without computing the field via > rnfkummer? I know about bnrgaloismat, but it doesn't seem as though > the resulting representation of the galois group can be used to find > the order of elements easily. Please give an example. Do you mean 'order' as in group theory or 'order' as in 'integral closure' ? 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. Cheers, Bill.