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Topic: [Mathqa]Re: Galois group of the rationals
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Gaetan Chenevier

Posts: 3
Registered: 12/13/04
[Mathqa]Re: Galois group of the rationals
Posted: Mar 5, 2001 2:21 PM
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> Is there an example of such a group?

Yes, take the subfield of C generated by all the square roots of integers,
call it K. K is Galois over Q and G=3DGal(K/Q) with its topology
is isomorphic to (Z/2Z)^I (I being an infinite countable set) with
pointwise topology.

Subgroups of index 2 in G which come from quadratic extensions of Q are
those corresponding to continuous linear forms on this Z/2Z vector space. But
there are non continuous one.



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