Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, 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.
Mashayekhy, B., Hokmabadi, A., & Mohammadzadeh, F. (2011). On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group. Bulletin of the Iranian Mathematical Society, 37(No. 4), 235-242.
MLA
B. Mashayekhy; A. Hokmabadi; F. Mohammadzadeh. "On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group". Bulletin of the Iranian Mathematical Society, 37, No. 4, 2011, 235-242.
HARVARD
Mashayekhy, B., Hokmabadi, A., Mohammadzadeh, F. (2011). 'On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group', Bulletin of the Iranian Mathematical Society, 37(No. 4), pp. 235-242.
VANCOUVER
Mashayekhy, B., Hokmabadi, A., Mohammadzadeh, F. On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group. Bulletin of the Iranian Mathematical Society, 2011; 37(No. 4): 235-242.