publication . Article . Preprint . 2013

filtrations of free groups as intersections

Efrat, Ido;
Open Access
  • Published: 06 Dec 2013 Journal: Archiv der Mathematik, volume 103, pages 411-420 (issn: 0003-889X, eissn: 1420-8938, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
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 Grun for the lower central filtration. In particular, we do this for the n-th term in the lower p-central filtration of S.
Subjects
arXiv: Mathematics::Algebraic GeometryMathematics::K-Theory and Homology
free text keywords: General Mathematics, Unipotent, Homomorphism, Mathematics, Filtration, law.invention, law, Topology, Free group, Matrix (mathematics), Mathematics - Group Theory, Primary 20E05 Secondary 20E18
22 references, page 1 of 2

[DDMS] J. D. Dixon, M. du Sautoy, A. Mann, and D. Segal, Analytic Pro-p Groups, Cambridge Stud. Adv. Math., vol. 61, Cambridge University Press, 1999.

[Efr13] I. Efrat, The Zassenhaus filtration, Massey products, and representations of profinite groups (2013), to appear, available at arXiv:1301.0896.

[EM11a] I. Efrat and J. Min´aˇc, On the descending central sequence of absolute Galois groups, Amer. J. Math. 133 (2011), 1503-1532.

[EM11b] I. Efrat and J. Min´aˇc, Galois groups and cohomological functors (2011), to appear, available at arXiv:1103.1508v2.

[FJ08] M. D. Fried and M. Jarden, Field arithmetic, 3rd ed., Springer, Berlin, 2008.

[Gru¨36] O. Gru¨n, U¨ber eine Faktorgruppe freier Gruppen I, Deutsche Mathematik 1 (1936), 772-782.

[Jen41] S. A. Jennings, The structure of the group ring of a p-group over a modular field, Trans. Amer. Math. Soc. 50 (1941), 175-185. [OpenAIRE]

[Koc60] H. Koch, U¨ber die Faktorgruppen einer absteigenden Zentralreihe, Math. Nach. 22 (1960), 159-161.

[Koc02] H. Koch, Galois theory of p-extensions, Springer-Verlag, Berlin, 2002.

[Mag35] W. Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), 259-280. [OpenAIRE]

[Mag37] W. Magnus, U¨ber Beziehungen zwischen ho¨heren Kommutatoren, J. reine angew. Math. 177 (1937), 105-115.

[MS96] J. Min´aˇc and M. Spira, Witt rings and Galois groups, Ann. Math. 144 (1996), 35-60.

[MT13] J. Min´aˇc and N. D. Tan, The Kernel Unipotent Conjecture and the vanishing of Massey products for odd rigid fields (2013), available at arXiv:1312.2655.

[Mor12] M. Morishita, Knots and primes, Universitext, Springer, London, 2012.

[NSW08] J. Neukirch, A. Schmidt, and K. Wingberg, Cohomology of Number Fields, Second edition, 2nd ed., Springer, Berlin, 2008.

22 references, page 1 of 2
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publication . Article . Preprint . 2013

filtrations of free groups as intersections

Efrat, Ido;