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

[nille40]

Hi!
Let us say we have a group \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&#039;t have 0 in the set of the group.<br /> <br /> If the tex stuff didn&#039;t show up, the group should be<br /> &lt;Z_n\{0},+&gt;<br /> <br /> Is this then not a group?<br /> 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.