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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.




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.




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.


Content:
Front Matter....Pages i-xxi
Lower Central Series....Pages 1-100
Dimension Subgroups....Pages 101-164
Derived Series....Pages 165-185
Augmentation Powers....Pages 187-227
Homotopical Aspects....Pages 229-290
Miscellanea....Pages 291-297
Back Matter....Pages 299-352


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.


Content:
Front Matter....Pages i-xxi
Lower Central Series....Pages 1-100
Dimension Subgroups....Pages 101-164
Derived Series....Pages 165-185
Augmentation Powers....Pages 187-227
Homotopical Aspects....Pages 229-290
Miscellanea....Pages 291-297
Back Matter....Pages 299-352
....
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