1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Group theory Q
  1. Group Theory Q (Replies: 3)

  2. Another Group theory Q (Replies: 7)

Loading...