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I'm reading basic algebra notes and met this exercise:

Let $\circ$ be an operator defined on $G$, if $\forall a,b,c$, $$ab=ac\Rightarrow b=c$$ and $$ba=ca\Rightarrow b=c$$ then $(G,\circ)$ is a group.

I couldn't figure this out. Could you pls give me some hint?

athos
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  • See here: http://math.stackexchange.com/questions/510157/show-that-g-is-a-group-if-g-is-finite-the-operation-is-associative-and-cancel?rq=1 – David Wheeler Mar 03 '15 at 02:34
  • just to mark the answer is here: http://math.stackexchange.com/a/748375/26632 – athos Mar 03 '15 at 11:53

1 Answers1

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This is false, consider the set of positive integers under addition as a counterexample.Although if you ask for $G$ to be associative and finite you do have a group.

Asinomás
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