Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let $G$ be a finite $p$-group of order $p^n$ with $|G'| = p^k$. Let $M(G)$ denotes the Schur multiplier of $G$. A classical result of Green states that $|M(G)| \leq p^{\frac{1}{2}n(n-1)}$. In 2009, Niroomand, improving Green's and other bounds on $|M(G)|$ for a non-abelain $p$-group $G$, proved that $|M(G)| \leq p^{\frac{1}{2}(n-k-1)(n+k-2)+1}$. In this article  note that a bound, obtained earlier, by Ellis and igold is more general than the bound of Niroomand.  derive from the bound of Ellis and igold that $|M(G)| \leq p^{\frac{1}{2}(d(G)-1)(n+k-2)+1}$ for a non-abelain $p$-group $G$. Moreover,  sharpen the bound of Ellis and igold and as a consequence derive that if $G^{ab}$ is not homocyclic then $|M(G)| \leq p^{\frac{1}{2}(d(G)-1)(n+k-3)+1}$.  further note an improvement in an old bound given by Vermani. Finally  note, for a $p$-group of coclass $r$, that $|M(G)| \leq p^{\frac{1}{2}(r^2-r)+kr+1}$. This improves a bound by Moravec.
['Pradeep K. Rai']
I am writing a research paper on a idea A note on the order of the Schur multiplier of p-groups
[{"from": "human", "value": "I am writing a research paper on a idea A note on the order of the Schur multiplier of p-groups"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let $G$ be a finite $p$-group of order $p^n$ with $|G'| = p^k$. Let $M(G)$ denotes the Schur multiplier of $G$. A classical result of Green states that $|M(G)| \\leq p^{\\frac{1}{2}n(n-1)}$. In 2009, Niroomand, improving Green's and other bounds on $|M(G)|$ for a non-abelain $p$-group $G$, proved that $|M(G)| \\leq p^{\\frac{1}{2}(n-k-1)(n+k-2)+1}$. In this article  note that a bound, obtained earlier, by Ellis and igold is more general than the bound of Niroomand.  derive from the bound of Ellis and igold that $|M(G)| \\leq p^{\\frac{1}{2}(d(G)-1)(n+k-2)+1}$ for a non-abelain $p$-group $G$. Moreover,  sharpen the bound of Ellis and igold and as a consequence derive that if $G^{ab}$ is not homocyclic then $|M(G)| \\leq p^{\\frac{1}{2}(d(G)-1)(n+k-3)+1}$.  further note an improvement in an old bound given by Vermani. Finally  note, for a $p$-group of coclass $r$, that $|M(G)| \\leq p^{\\frac{1}{2}(r^2-r)+kr+1}$. This improves a bound by Moravec."}]