Filtrations of free groups as intersections

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For several natural filtrations of a free group S, we express the n-th term of the filtration as the intersection of all kernels of homomorphisms from S to certain groups of upper-triangular unipotent matrices. This generalizes a classical result of Grün for the lower central filtration. In particular, we do this for the n-th term in the lower p-central filtration of S.

Original languageEnglish
Pages (from-to)411-420
Number of pages10
JournalArchiv der Mathematik
Issue number5
StatePublished - 25 Nov 2014


  • Primary 20E05
  • Secondary 20E18

ASJC Scopus subject areas

  • General Mathematics


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