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Question about algebraic groups

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data
    According to wikipedia, one of the requirements of group is:
    For all a, b in G, the result of the operation, a • b, is also in G.

    So say we have 2 (2x2) matricies as elements of a group:
    [itex]\frac{0|1}{1|0}[/itex] and [itex]\frac{w|0}{0|w^{2}}[/itex]
    and the product [itex]\frac{0|1}{1|0}[/itex] • [itex]\frac{w|0}{0|w^{2}}[/itex] is [itex]\frac{0|w^{2}}{w|0}[/itex]

    does this mean that the matrix [itex]\frac{0|w^{2}}{w|0}[/itex] also has to be an element of that group or does it mean that the elements of the matrix itself (0,w,[itex]w^{2}[/itex]) have to just generally exist?
     
  2. jcsd
  3. Mar 28, 2012 #2

    Dick

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    "the result of the operation, a • b, is also in G" is pretty unambiguous. It has to be an element of the group.
     
  4. Mar 28, 2012 #3

    tiny-tim

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    hi xago! :wink:
    yes :smile:
     
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