#### Volume 10, issue 1 (2010)

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Homotopy nilpotent groups

### Georg Biedermann and William G Dwyer

Algebraic & Geometric Topology 10 (2010) 33–61
##### Abstract

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define homotopy $n$–nilpotent groups as homotopy algebras over certain simplicial algebraic theories. This notion interpolates between infinite loop spaces and loop spaces, but backwards. We study the relation to ordinary nilpotent groups. We prove that $n$–excisive functors of the form $\Omega F$ factor over the category of homotopy $n$–nilpotent groups.

##### Keywords
Goodwillie tower, excisive functors, loop group, lower central series, loop space, infinite loop spaces, homotopy nilpotent groups, algebraic theories
##### Mathematical Subject Classification 2000
Primary: 55P47, 55U35
Secondary: 18C10, 55P35