Filtrations of free groups arising from the lower central series

Michael Chapman, Ido Efrat

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We make a systematic study of filtrations of a free group F defined as products of powers of the lower central series of F. Under some assumptions on the exponents, we characterize these filtrations in terms of the group algebra, the Magnus algebra of non-commutative power series, and linear representations by upper-triangular unipotent matrices. These characterizations generalize classical results of Grün, Magnus, Witt, and Zassenhaus from the 1930s, as well as later results on the lower p-central filtration and the p-Zassenhaus filtrations. We derive alternative recursive definitions of such filtrations, extending results of Lazard. Finally, we relate these filtrations to Massey products in group cohomology.

Original languageEnglish
Pages (from-to)405-433
Number of pages29
JournalJournal of Group Theory
Volume19
Issue number3
DOIs
StatePublished - 1 May 2016

ASJC Scopus subject areas

  • Algebra and Number Theory

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