G is a p-group -
$|G| = p^a$
p is prime
i need to find the factor groups of G and prove that it is solvable.
what i tried -
EDITED: after watching the comments and investigating I know every element of G is of order $p^i$ where $i<a $.
I try to prove that G is solvable by induction on a.
where $|G| = p^a$
if a = 1 then G is cyclic with prime order so its solvable. and the factors are $G/1$
if a>1 then $G/Z$ is trivial or of order less then a . if it is trivial then what does it mean? and if it is of order less then a then i know G/Z is solvable (from the induction) but how does it help me know G is solvable? and in this case - what are the factor groups?
many thanks
any help will be very appreciated .