On the Schur multipliers of finite p-groups of given coclass

In this paper we obtain bounds for the order and exponent of the Schur multiplier of a p-group of given coclass. These are further improved for p-groups of maximal class. In particular, we prove that if G is p-group of maximal class, then |H ₂(G, ℤ)| < |G| and expH ₂(G, ℤ) ≤ expG. The bound for the order can be improved asymptotically.