Results 1 to 2 of 2

Math Help - isomorphism type question

  1. #1
    nhk
    nhk is offline
    Junior Member
    Joined
    Apr 2010
    Posts
    43

    isomorphism type question

    I got that|G|=40 and |Z(G)| contains an element of order 2. From Lagrange i know that the order of Z(G) must divide |G| and be a multiple of 2. I am able to do all the cases by the G/Z theorem accept for 1 case. This is the case where |Z(G)|=2. Then I get |G/Z(G)| =20, and I cant use one of the nice theorms like the 2p theorem or the p^2 theorem to get the isomorphism type. Does anyone have any ideas on what I should do?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by nhk View Post
    I got that|G|=40 and |Z(G)| contains an element of order 2. From Lagrange i know that the order of Z(G) must divide |G| and be a multiple of 2. I am able to do all the cases by the G/Z theorem accept for 1 case. This is the case where |Z(G)|=2. Then I get |G/Z(G)| =20, and I cant use one of the nice theorms like the 2p theorem or the p^2 theorem to get the isomorphism type. Does anyone have any ideas on what I should do?
    Off the top of my head, it has even order and a centre of order 2 - surely it is just D_{40}? Certainly, this is a group with the correct properties. There may be other groups with these properties though, I've not quite got enough time to look at this properly. Sorry!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. isomorphism type question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 1st 2010, 04:52 PM
  2. Need help with NCR type question??
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: April 15th 2010, 07:52 PM
  3. Super stuck on Type 1 and Type 2 errors
    Posted in the Statistics Forum
    Replies: 0
    Last Post: January 29th 2010, 01:06 PM
  4. Probability question involving (A given B type question )
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 9th 2009, 10:08 AM
  5. Type 1/ Type 2 Error Question
    Posted in the Statistics Forum
    Replies: 4
    Last Post: August 3rd 2008, 07:51 AM

Search Tags


/mathhelpforum @mathhelpforum