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

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Let G be a p-group of nilpotency class k with finite exponent (G) and let m=ₚk. We show that (M⁽ᶜ⁾(G)) divides (G)pᵐ⁽ᵏ⁻¹⁾, for all c≥1, where M⁽ᶜ⁾(G) denotes the c-nilpotent multiplier of G. This implies that (M(G)) divides (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.