The following is taken from M.A. Armstrong's Groups & Symmetry, #15.6
If $H,J$ are normal subgroups of a group $G$, and if they only have the identity element in common, show that $xy=yx$ for all $x\in H, y\in J$.
This question looks so easy, but I cannot seem to answer it. Since $H,J$ are normal, $yH=Hy$ and $xJ=Jx$, and $yh=h'y$ for $h,h'\in H$ and $xj=j'x$ for $j,j'\in J$. I'm missing the hypothesis $H\cap J = \{{e}\}$. How does this figure?
