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Homework Help: Group theory Q

  1. Mar 3, 2006 #1
    The question reads :

    "What is the order of a group G generated by elements a and b subject only to the relations

    [tex] a^7 = 1 [/tex] , [tex] b^3 = 1 [/tex] , [tex] ba = a^rb [/tex]"

    I know that the order is the number of elements in the group.

    I'm having a lot of trouble answering a lot of these questions.
    Any help would be greatly appreciated.

    Thanks in advance.
     
  2. jcsd
  3. Mar 3, 2006 #2

    Hurkyl

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    Well, you could always write down all of the elements of the group.
     
  4. Mar 3, 2006 #3
    How do you go about doing that using the information given? I don't know where to begin.

    Also, does [itex] a^7 = 1 [/itex] mean a to the 7 is equal to the identity element?
     
  5. Mar 3, 2006 #4

    Hurkyl

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    Well, there's a, and aa, and aaa, and ab, and ba, and aba, and bab, and abbaabbab, and...


    Yes, the relation a^7 = 1 means that aaaaaaa is the identity.
     
  6. Mar 3, 2006 #5
    I think I see where this is going.

    Does [itex]a^8 = a^7 * a = 1 * a[/itex] make sense?
     
  7. Mar 3, 2006 #6
    Yup. And use the ba relation to reorder your products so that they all read "aaaa....bb..."

    -Dan
     
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