1
$\begingroup$

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 $\mathbb Q$.)

  • 0
    I assume $Q$ is the rationals, but what is $Q^a$?2012-11-15
  • 0
    Algebraic Closure of Q.2012-11-15
  • 0
    Using 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
  • 1
    No. 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
  • 0
    So, that makes only non trivial torsion elements are of order 2, and conjugates of conjugation..2012-11-15

1 Answers 1