Closely related to the lower central series of a group is its derived series. We first give a method, due to Gupta-Passi [Gup07], for studying the derived series of free nilpotent groups. Our main aim in this Chapter, however, is the study of the transfinite terms of the derived series of groups. We give an account of the homological approach of R. Strebel [Str74]. The impact on the asphericity conjecture of J. H. C. Whitehead [Whi41] is also explored.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Derived Series. In: Lower Central and Dimension Series of Groups. Lecture Notes in Mathematics, vol 1952. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85818-8_3
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DOI: https://doi.org/10.1007/978-3-540-85818-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85817-1
Online ISBN: 978-3-540-85818-8
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