A fundamental object of study in group theory is the lower
central series of groups. Understanding its relationship with the
dimension series, which consists of the subgroups determined by the
augmentation powers, is a challenging task. This monograph presents
an exposition of different methods for investigating this
relationship. In addition to group theorists, the results are also
of interest to topologists and number theorists. The approach is
mainly combinatorial and homological. A novel feature is an
exposition of simplicial methods for the study of problems in group
theory.
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