On a conjecture of a bound for the exponent of the Schur multiplier of a finite p-group

Let G be a p-group of nilpotency class k with finite exponent exp(G) and let m=floor log pk floor. We show that exp(M^{(c)}(G)) divides exp(G)p^{m(k-1)}, for all c ≥1, where M^{(c)}(G) denotes the c-nilpotent multiplier of G. This implies that exp( M(G)) divides exp(G), for all finite p-groups of class at most p-1. Moreover, we show that our result is an improvement of some previous bounds for the exponent of M^{(c)}(G) given by M. R. Jones, G. Ellis and P. Moravec in some cases.