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Finite Group

  1. Nov 25, 2003 #1
    Hi!
    Let us say we have a group [tex]\langle Z_n \backslash \lbrace 0 \rbrace, \cdot \rangle[\tex] and one element multiplied with another gives kn. n divides kn, so kn equals 0. But we don't have 0 in the set of the group.

    If the tex stuff didn't show up, the group should be
    <Z_n\{0},+>

    Is this then not a group?
    Nille
     
  2. jcsd
  3. Nov 25, 2003 #2
    You re damn straight its not a group!!! a group contains the identity! remove the identity, and you no longer have a group on your hands... but why would you want to go and do something so perverse like remove the identity?
     
  4. Nov 25, 2003 #3
    Even worse, it's not closed under addition. 1+(-1)=0, which is not an element in the given set.
     
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