A lower bound on the size of maximal abelian subgroups

Let G be a p-group for some prime p. Let n be the positive integer so that |G: Z (G) | = pⁿ. Suppose A is a maximal abelian subgroup of G. Let pˡ = max \|Z (CG (g) ): Z (G) |: g G Z (G) \, pᵇ = max \|cl (g) |: g G Z (G) \, and pᵃ = |A: Z (G) |. Then we show that a n/ (b+l).