Results 1 to 5 of 5

Math Help - groups

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    4

    groups



    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2007
    Posts
    4
    Can anyone help here?

    Do I make a Cayley table? If so, Im confused how to traverse the permutation. If I start at (15)(24), it goes 1 to 5, 5 to 4, 4 to 1 ... is this correct for first step?

    thanks
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,395
    Thanks
    1481
    Awards
    1
    Quote Originally Posted by theory07 View Post
    If so, Im confused how to traverse the permutation. If I start at (15)(24), it goes 1 to 5, 5 to 4, 4 to 1 ... is this correct for first step?
    No. Lets write in traditional notation.
    \left( {15} \right)\left( {24} \right) = \left( {\begin{array}{*{20}c}<br />
   1 & 2 & 3 & 4 & 5 & 6  \\<br />
   5 & 4 & 3 & 2 & 1 & 6  \\<br />
\end{array}} \right)<br />

    1 to 5, 5 to 1; 2 to 4, 4 to 2. The 3 & 6 are inactive.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2007
    Posts
    4
    Is that why it makes a group, because whatever number you start from, you always get back to the same number.. so you just get e. ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,395
    Thanks
    1481
    Awards
    1
    Quote Originally Posted by theory07 View Post
    Is that why it makes a group, because whatever number you start from, you always get back to the same number.. so you just get e. ?
    I don't understand what you mean. But I will tell you this.
    First, you should have known about cycle notation before even tackling this problem.
    You also should how to show that a subset of a group is a subgroup of the group.
    In order to show that a subset H of G is a subgroup you must show that the identity is in H and that H is closed with respect to the group operation and group inverse.
    Constructing a group table is one possible way to proceed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. About minimal normal groups and subnormal groups
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: October 20th 2011, 01:53 PM
  2. Automorphism groups of cyclic groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: August 15th 2011, 09:46 AM
  3. Quotient Groups - Infinite Groups, finite orders
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: August 11th 2010, 07:07 AM
  4. free groups, finitely generated groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 23rd 2009, 03:31 AM
  5. Order of groups involving conjugates and abelian groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 5th 2009, 08:55 PM

Search Tags


/mathhelpforum @mathhelpforum