How to find non trivial torsion elements in $\operatorname{Gal}(\mathbb Q^a /\mathbb Q) $? One element will be conjugation, but is there any other non trivial torsion element? (Here $\mathbb Q^a$ denotes the algebraic closure of $\mathbb Q$.)
Torsion elements in $\operatorname{Gal}(\mathbb Q^a /\mathbb Q) $
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abstract-algebra
galois-theory
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0I assume $Q$ is the rationals, but what is $Q^a$? – 2012-11-15
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0Algebraic Closure of Q. – 2012-11-15
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0Using Artin Schreier Theorem, can I say Algebraic Closure of Q is Q(i) hence, Gal group contains only two elements, identity and conjugation? – 2012-11-15
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1No. Q(i) is not algebraically closed. What you can say based on the Artin-Schreier-theorem is that any torsion element of $Gal( \mathbb Q^a /\mathbb Q)$ has an order $\leq 2$. – 2012-11-15
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0So, that makes only non trivial torsion elements are of order 2, and conjugates of conjugation.. – 2012-11-15