Assertion: free abelian group | /r/HasProperty | $f$
Facets:
Source sentences:
text: You have to take the free Abelian group $F$ on generator set $\{x_1,x_2,x_3\}$ (which is isomorphic to $\Bbb Z^3$) and take its quotient by the subgroup $H$ generated by the given elements, so in particular we will have $$4[x_1]+4[x_2]+8[x_3]\ =\ 0$$ in this group $G=F/H$, and the other two elements give rise to similar equations.