Filtrations of free groups as intersections

Ido Efrat

doi:10.1007/s00013-014-0701-x

Filtrations of free groups as intersections

Ido Efrat

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	American English
Pages (from-to)	411-420
Number of pages	10
Journal	Archiv der Mathematik
Volume	103
Issue number	5
DOIs	https://doi.org/10.1007/s00013-014-0701-x
State	Published - 25 Nov 2014

Keywords

Primary 20E05
Secondary 20E18

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00013-014-0701-x

Cite this

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title = "Filtrations of free groups as intersections",

abstract = "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 Gr{\"u}n for the lower central filtration. In particular, we do this for the n-th term in the lower p-central filtration of S.",

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N2 - 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.

AB - 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.

KW - Primary 20E05

KW - Secondary 20E18

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U2 - 10.1007/s00013-014-0701-x

DO - 10.1007/s00013-014-0701-x

M3 - Article

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EP - 420

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 5

ER -

Filtrations of free groups as intersections

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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