A partial extension of Lazard's correspondence for finite $p$-groups

M. Lazard established a correspondence between finitep-groups of nilpotence class less than p and finite nilpotent Lie rings of p-power order and nilpotence class less than p. This correspondence has had many applications, but cannot generally be extended top-groups of classp or larger. However, in this paper, we obtain a partial extension of Lazard's result for ap-group that is a product of normal subgroups of class less thanp. Mathematics Subject Classification (2000). 20D15, 20F18, 20F40.