Let K/F be an infinite Galois extension, and let N be a normal sub-group of Gal(K/F). Show that N closure is a normal subgroup of Gal(K/F).
Closure of Normal Subgroups of the Galois Group for an Infinite Galois Extension is Normal
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abstract-algebra
group-theory
field-theory
galois-theory
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1the closure of a normal subgroup in any topological group is normal – 2012-10-31
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0I have this proof. But can we do it w/o topological group? – 2012-10-31
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0Without topology, what do you mean by closure? – 2012-11-02
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0I am seeking a proof using Fundamental Theorem of Infinite Galois Theory. Possibly by showing Fixed field of N closure is Galois over F. – 2012-11-02
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0Okay!! I have got it. Thanks, anyway! – 2012-11-06