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Filtrations of free groups as intersections

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 Grun for the lower central filtration. In particular, we do this for the n-th term in the lower p-central filtration of S.

preprint2014arXivOpen access
Ido Efrat
math.GR
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Ido Efrat

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