For the free group, it is called the Zassenahus filtration. Golod-Shafarevich groups are defined in terms of it. Ershov's survey 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
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