\author{Dave Benson} \author{John Greenlees} \title{Massey products in the homology of the loopspace of a $p$-completed classifying space: finite groups with cyclic Sylow $p$-subgroups} \begin{document} \begin{abstract} Let $G$ be a finite group with cyclic Sylow $p$-subgroup, and let $k$ be a field of characteristic $p$. Then $H^*(BG;k)$ and $H_*(\Omega BG\phat;k)$ are $A_\infty$ algebras whose structure we determine up to quasi-isomorphism. \end{abstract}