Bill Allombert on Thu, 8 May 2003 23:00:28 +0200

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Re: polredabs() suggestion

On Tue, May 06, 2003 at 03:01:52PM -0400, Igor Schein wrote:
> Hi,
> I am just curious, what is the mathematical reasoning behind the fact
> that the fields with a huge number of subfields ( the ones that give
> polredabs() hard time ), are either dihedral or compositums or
> dihedral fields? 

Subfields are linked with subgroups of the Galois group. 
The family of groups with the largest number of subgroups
is (Z/2Z)^n, so I do not think the above assertion is true in general.

Though for the purpose of polredabs, groups having a lot of *isomorphic*
subfields, like dihedral groups and unlike abelian groups, may be worst cases.