Results 1 to 5 of 5

Math Help - Klein four-group is no cyclic

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    461

    Klein four-group is no cyclic

    Proof:
    The Klein four-group (tableau: )  \begin{pmatrix}\circ & e & a & b & c\\ \hline e&e&a&b&c\\ a&a&e&c&b\\ b&b&c&e&a\\ c&c&b&a&e \end{pmatrix} is not a cyclic group

    First I thought it is not cyclic because the Klein four-group is not commutative, but according to the tableau my guess is wrong.

    Any help is much appreciated.

    Rapha
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    From
    Paris
    Posts
    354
    Look at the order of each element!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Quote Originally Posted by clic-clac View Post
    Look at the order of each element!
    The order of each element is 2, but there are 4 elements

    thats why the group is not cyclic?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Nov 2008
    From
    Paris
    Posts
    354
    Yep! Let G be a cyclic group, \exists x \in G / <x>=G
    Then x has the same order as G.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi clic-clac,

    Quote Originally Posted by clic-clac View Post
    Yep! Let G be a cyclic group, \exists x \in G / <x>=G
    Then x has the same order as G.
    Merci beaucoup
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Klein Four Group
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: April 1st 2011, 05:37 AM
  2. Genetic code of Klein four-group
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 6th 2010, 04:30 AM
  3. Klein 4-group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 25th 2010, 06:12 AM
  4. Klein four-group is normal group of A4
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: December 29th 2009, 03:15 PM
  5. Prove cyclic subroups => cyclic group
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: October 11th 2009, 08:36 PM

Search Tags


/mathhelpforum @mathhelpforum