Let G be a p -group of nilpotency class
k with finite exponent exp(G) and let m= lfloor log_pk rfloor . We show that exp(M^{(c)}(G)) divides
exp(G)p^{m(k-1)} , for all c geq1 , 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.
کلید واژگان :
Schur multiplier, Nilpotent multiplier, Exponent, Finite p -groups.
