Finite Group

[nille40]

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

[lethe]

Originally posted by nille40


Is this then not a group?
Nille

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?

[Lonewolf]

Even worse, it's not closed under addition. 1+(-1)=0, which is not an element in the given set.