On a Conjecture of a Bound for the Exponent of the Schur Multiplier of a Finite $p$-Group

Abstract

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $\exp (G)$ and let $m=\lfloor {\log }_{p}k\rfloor$. We show that $\exp (M^{(c)}(G))$ divides $\exp (G)p^{m(k-1)}$, for all $c\ge 1$, 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.

arXiv comment8 pages, to appear in Bulletin of the Iranian Mathematical Society

References in corpus (1)

• Some Inequalities for Nilpotent Multipliers of Powerful $p$-Groups

Cited by in corpus (5)

• Some Inequalities for Nilpotent Multipliers of Powerful $p$-Groups
• On the Exponent Conjectures
• On the Exponent of the Schur Multiplier
• On the exponent conjecture of Schur
• On the Exponent of the Schur multiplier of a Pair of Finite $p$-Groups