Results 1 to 2 of 2

Math Help - When is GL(V) finite?

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    18

    When is GL(V) finite?

    If V has finite dimension does this imply that GL(V) is finite?
    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 Smancer View Post
    If V has finite dimension does this imply that GL(V) is finite?
    If V is a finite dimensional vector space over the field F say of degree n. Then there is an vector space isomorphism \theta : V\to F^n. Therefore, \text{GL}(V) is isomorphic to \text{GL}(n,F) which is a finite group.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Distinct Bases for Finite Vector Spaces over Finite Fields
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 29th 2011, 12:31 PM
  2. Replies: 1
    Last Post: May 21st 2011, 04:17 AM
  3. Replies: 7
    Last Post: February 19th 2011, 03:29 PM
  4. Replies: 1
    Last Post: October 15th 2008, 11:34 AM
  5. Finite size if finite number of subgroups
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: March 9th 2006, 12:32 PM

Search Tags


/mathhelpforum @mathhelpforum