The higher lower central series

Abstract

The Baer invariants Γ n (G) of a group are central extensions of the elementsγ n (G) of the lower central series. We show that the inclusionsγ n +1 ⊂γ n can be lifted to functor morphisms Γ n+1→Γ n and a canonical Lie algebra, analogous to Lazard’s Lie algebra, can be constructed which is explicitly computable. This is applied in various ways.