A note on the order of the Schur multiplier of p-groups

作者：Rai Pradeep K^*

来源：International Journal of Algebra and Computation, 2017, 27(5): 495-500.

DOI：10.1142/S0218196717500254

• Schur multiplier
• finite p-group
• coclass

Let G be a finite p-group of order p(n) with |G'|=p(k), and let M(G) denote its Schur multiplier. A classical result of Green states that |M(G)|<= p(1/2n(n-1)). In 2009, Niroomand, improving Green's and other bounds on |M(G)| for a non-abelian p-group G, proved that |M(G)|<= p(1/2(n-k-1)(n+k-2)+1). In this paper, we prove that a bound, obtained earlier by Ellis and Wiegold, is stronger than that of Niroomand. We derive from the bound of Ellis and Wiegold that |M(G)|<= p(1/2(d(G)-1)(n+k-2)+1) for a non-abelian p-group G. We obtain an improvement to an old bound given by Vermani. Finally we prove, for a p-group of coclass r, that |M(G)|<= p(1/2(r2-r)+kr+1). This improves a bound by Moravec.

• 出版日期2017-8