Can you explain/prove, why the number of minimal normal subgroups of an elementary abelian $p$-group of order $p^n$ (for instance of $\mathbb{Z_p}^n$), is exactly $(p^n-1)/(p-1)$?
I know that it seems trivial but i can't see why. It is an exercise from Dixon & Mortimer book "Permutation Groups" pg.120.