|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. Cheers, Bill.