A bound for the derived and Frattini subgroups of a prime-power group
Proc. Amer. Math. Soc. 126 (1998), 2513-2523. 

Graham Ellis
Department of Mathematics, University College, Galway, Ireland 

Abstract. This paper is based on the seemingly new observation that the Schur 
multiplier $M(G)$ of a $d$-generator group of prime-power order $p^n$ has 
order $|M(G)\le p^{d(2n-d-1)/2}$. We prove several related results, 
including sufficient conditions for a sharper bound on $|M(G)$ to be an 
equality.