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 Sheila496 October 20th, 2011 09:45 AM

About minimal normal groups and subnormal groups

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

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

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

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