(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove, that a senigruop S is a group if and only if for every x in S there exists a unique x' in S so that xx'x=x.

2. Relevant equations

3. The attempt at a solution

I am trying to prove that xx'=1_{S}for all x in S. But all I can show is that xx' is in E_{S}={x | x^2=x} for every x in S. I am having a lot of troubles proving xx'=yy' and I can't even prove that 1_{S}si in S. Am I going in the right direction?

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# Homework Help: Prove a semigroup is a group

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