I'm having some problems with understanding the corollary of the next theorem :
Every minimal normal subgroup $K$ of $G$ is a direct product $K = T_1 \times T_2 \times \cdots \times T_k$ where the $T_i$ are simple normal subgroups of $K$ which are conjugate under $G$.
The corollary states :
Every minimal normal subgroup of a finite group is either an elementary abelian p-group for some prime p, or its centre is equal to 1.
I don't understand what from the theorem implies the statement of the corollary. If someone could give me a hint I would be thankful.