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Topic:
[Mathqa]Re: Galois group of the rationals
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[Mathqa]Re: Galois group of the rationals
Posted:
Mar 5, 2001 2:21 PM


> 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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