Why is $V_1$ a $p$-group

Question

I am reading a proof. The argument is like this:

Let $p$ be a prime.

1. $V_0\supseteq V_1\supseteq\dots\supseteq V_m=1$
2. $V_0/V_1$ is a cyclic group.
3. For $j\geq 2$, $V_{j-1}/V_j$ is an elementary abelian $p$-group (or equivalently a vector space over $F_p$)

Then it says that $V_1$ is a $p$-group. Why is this true ?

Answer 1

Its size $|V_1|=[V_1:V_2]\cdots[V_{m-1}:V_m]$ is a product of powers of $p$.