# Tag Info

### If $G=AB$ and $|G|=|A||B|$, then $G=A^{-1}B$.
Maps between finite sets with the same cardinality are injective iff surjective. Because of $|G|=|A||B|=|A\times B|$, such a map is $\phi\colon A\times B\rightarrow G,(a,b)\mapsto ab$. It is ...