For the free group, it is called the Zassenahus filtration. Golod-Shafarevich groups are are defined in terms of it. [Ershov's survey][1] on Golod-Shafarevich groups is excellent. Highly recommended. It is published as  Ershov, Mikhail Golod-Shafarevich groups: a survey. Internat. J. Algebra Comput. 22 (2012), no. 5, 1230001, 68 pp


  [1]: http://front.math.ucdavis.edu/1206.0490