Consider L is an ideal in $g/ g '$ of codimension 1.
Let $ \pi: g \longrightarrow g / g '$ homomorph be canonical. So,
- $ \pi^{-1} (L)$ um is ideal in g.
In fact, if $x \in \pi^{-1}(L)$ and $\in g$, then
$$\pi[x,y]=[\pi(x), \pi(y)]=0 \in L$$
because $g/g'$ is abelian and $\pi(L) \in L \subset g/g'$. So $ [x, y] \in \pi ^ {- 1} (L) $.
- $ \pi^{-1}(L) $ have codimension 1.
i need to know if 1. is correct and how to do item 2.