Is <Z_n\{0},+> a Group Without Zero?

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The discussion centers on the mathematical structure and its classification as a group. It is established that this set cannot be considered a group because it lacks an identity element and is not closed under addition. Specifically, the operation 1 + (-1) results in 0, which is excluded from the set. Therefore, fails to meet the fundamental criteria required for a group.

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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.<br /> <br /> If the tex stuff didn't show up, the group should be<br /> <Z_n\{0},+><br /> <br /> Is this then not a group?<br /> Nille[/tex]
 
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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?
 
Even worse, it's not closed under addition. 1+(-1)=0, which is not an element in the given set.
 

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