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Groups and Subgroups

  1. May 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Thus far in my studying I've been able to at least have a sense of where to start solving the problems... until now.

    Find the order of the subgroup of the multiplicative group G of 4x4 matrice generated by:

    | 0 1 0 0 |
    | 0 0 0 1 |
    | 0 0 1 0 |
    | 1 0 0 0 |

    Recall the identity e:

    | 1 0 0 0 |
    | 0 1 0 0 |
    | 0 0 1 0 |
    | 0 0 0 1 |

    2. Relevant equations

    3. The attempt at a solution

    No clue, whatsoever. :(
     
  2. jcsd
  3. May 12, 2009 #2
    Call your matrix A. What's A3?
     
  4. May 12, 2009 #3
    I'm not sure? =(
     
  5. May 12, 2009 #4

    Dick

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    What do you mean, "I'm not sure"? Cube the matrix, i.e. multiply it by itself three times. Then you'll know what A^3 is. You aren't giving VKint the help deserved of the clue.
     
  6. May 12, 2009 #5
    Ok, had to remember how to multiply matrices. I got the identity, e.
     
  7. May 12, 2009 #6

    Dick

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    So did I. Problem solved, right?
     
  8. May 12, 2009 #7
    I don't quite understand. So is the order 3 because that's how many times I had to multiply it by itself to get the identity?
     
  9. May 12, 2009 #8

    Dick

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    A isn't the identity, A^2 isn't the identity, A^3 is. So yes, the order is 3. Look up 'order of a group element'.
     
  10. May 12, 2009 #9
    Awesome, thanks.
     
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