Results 1 to 2 of 2

Math Help - automorphism

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    154

    automorphism

    If  \sigma_{1}, \sigma_2, \ldots, \sigma_{n} is a group of automorphisms of a field  E and if  F is a fixed field of  \sigma_{1}, \sigma_{2}, \ldots,  \sigma_{n}, then  (E/F) = n .

    How would I prove this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by heathrowjohnny View Post
    If  \sigma_{1}, \sigma_2, \ldots, \sigma_{n} is a group of automorphisms of a field  E and if  F is a fixed field of  \sigma_{1}, \sigma_{2}, \ldots,  \sigma_{n}, then  (E/F) = n .
    There is a result due to Artin . Let G be a finite group of automorphism of E, let F=E^G be the fixed subfield, then E/F is finite and [E:F] \leq |G|. Note, you need the \leq sign.
    Last edited by ThePerfectHacker; March 1st 2008 at 07:35 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Automorphism
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: August 22nd 2010, 11:39 PM
  2. Automorphism
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: December 11th 2009, 06:16 PM
  3. Automorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 21st 2009, 11:48 AM
  4. AutoMorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 31st 2008, 05:28 AM
  5. Automorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 19th 2008, 07:03 AM

Search Tags


/mathhelpforum @mathhelpforum