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Math Help - Question on Groups

  1. #1
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    Question on Groups

    Please could a member run me through this question and help me understand it?
    Last edited by JohnGiles5; August 28th 2012 at 03:53 AM.
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  2. #2
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    Re: Question on Groups

    How is the operation * defined? It can't be standard multiplication, could you post the entire question?
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  3. #3
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    Re: Question on Groups

    Quote Originally Posted by hairymclairy View Post
    How is the operation * defined? It can't be standard multiplication, could you post the entire question?
    .
    Last edited by JohnGiles5; August 28th 2012 at 03:53 AM.
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  4. #4
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    Re: Question on Groups

    For part iii you simply need to fill in the table according to how * and \circ are defined. For example take the third row of the composition table. In the fourth column you need to enter 3\circ 4=3*4 (\mod 6). Now we have 3*4=3+4+1=8 and the remainder of 8 when we divide it by 6 is 2. So the entry in the third row and fourth column of the table is 2. You can use some of the previous parts of the question to make your life easier too- think about how the commutativity of * effects the elements of G under \circ

    For part iv you need to work out which element is the identity element of G. Then for each a\in G there will exist an integer m such that a^m is the identity element of G. You need to find m for each element a\in G by repeatedly composing a with itself until you get to the identity element.

    Once you know the order of each element finding all subgroups of G should be straightforward. Don't forget to use Lagrange- the order of any subgroup divides the order of the group.
    Last edited by hairymclairy; August 28th 2012 at 02:31 AM.
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    Re: Question on Groups

    Thanks very much for your help.
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