Hello everybody, I would like to have some help with these two questions:

1. Let $\displaystyle G$ be a finite nilpotent group and $\displaystyle N$ a minimal normal subgroup. Show that $\displaystyle N\leq Z(G)$.

2. Let $\displaystyle G$ be a group and $\displaystyle S,T$ verifying $\displaystyle S\neq T$ non-abelian subnormal subgroups of $\displaystyle G$. Prove that $\displaystyle st=ts$ $\displaystyle \forall s\in S$ $\displaystyle \forall t\in T$

1. I have already proved that $\displaystyle N$ must be abelian; $\displaystyle N\leq Z(N)$, but I find no way of proving that $\displaystyle N\leq Z(G)$ using that the nilpotency of $\displaystyle G$ and each one of its characterizations. Any idea?

Regards and thanks in advance.

Sheila.