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Mat. Zametki, 2006, Volume 79, Issue 3, Pages 409–419 (Mi mz2710)  

This article is cited in 7 scientific papers (total in 7 papers)

How to generalize known results on equations over groups

A. A. Klyachko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Known facts about the solvability of equations over groups are considered from a more general point of view. The theorem about the solvability of unimodular equations over torsion-free groups is generalized. A special case of the generalization is a multivariable version of this theorem. For unimodular equations over torsion-free groups, an analog of Magnus' Freiheitssatz is proved, which asserts the existence of a solution exhibiting good behavior with respect to the free factors of the initial group.

DOI: https://doi.org/10.4213/mzm2710

Full text: PDF file (239 kB)
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English version:
Mathematical Notes, 2006, 79:3, 377–386

Bibliographic databases:

UDC: 512.543.7
Received: 22.12.2003
Revised: 29.08.2005

Citation: A. A. Klyachko, “How to generalize known results on equations over groups”, Mat. Zametki, 79:3 (2006), 409–419; Math. Notes, 79:3 (2006), 377–386

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ant. A. Klyachko, “$SQ$-universality of one-relator relative presentations”, Sb. Math., 197:10 (2006), 1489–1508  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. A. Klyachko, “Free subgroups of one-relator relative presentations”, Algebra and Logic, 46:3 (2007), 158–162  mathnet  crossref  mathscinet  zmath  isi
    3. Klyachko A.A., “The structure of one-relator relative presentations and their centres”, J. Group Theory, 12:6 (2009), 923–947  crossref  mathscinet  zmath  isi  elib  scopus
    4. D. V. Baranov, Ant. A. Klyachko, “Economical adjunction of square roots to groups”, Siberian Math. J., 53:2 (2012), 201–206  mathnet  crossref  mathscinet  isi
    5. Klyachko A.A., Lurye D.E., “Relative Hyperbolicity and Similar Properties of One-Generator One-Relator Relative Presentations with Powered Unimodular Relator”, J. Pure Appl. Algebr., 216:3 (2012), 524–534  crossref  mathscinet  zmath  isi  elib  scopus
    6. Klyachko A., Thom A., “New topological methods to solve equations over groups”, Algebr. Geom. Topol., 17:1 (2017), 331–353  crossref  mathscinet  zmath  isi  elib  scopus
    7. Ivanov S.V., Klyachko A.A., “Quasiperiodic and Mixed Commutator Factorizations in Free Products of Groups”, Bull. London Math. Soc., 50:5 (2018), 832–844  crossref  zmath  isi  scopus
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