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Algebra Logika, 2005, Volume 44, Number 4, Pages 399–437 (Mi al124)  

This article is cited in 6 scientific papers (total in 6 papers)

The Kervaire – Laudenbach Conjecture and Presentations of Simple Groups

A. A. Klyachko

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

Abstract: The statement “no non-Abelian simple group can be obtained from a non-simple one by adding one generator and one relator” first is equivalent to the Kervaire – Laudenbach conjecture, and second, becomes true under the additional assumption that an initial non-simple group is either finite or torsion free.

Keywords: Kervaire – Laudenbach conjecture, relative presentation, simple group, car motion, cocar comotion

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English version:
Algebra and Logic, 2005, 44:4, 219–242

Bibliographic databases:

UDC: 512.543.7
Received: 18.11.2004

Citation: A. A. Klyachko, “The Kervaire – Laudenbach Conjecture and Presentations of Simple Groups”, Algebra Logika, 44:4 (2005), 399–437; Algebra and Logic, 44:4 (2005), 219–242

Citation in format AMSBIB
\Bibitem{Kly05}
\by A.~A.~Klyachko
\paper The Kervaire~-- Laudenbach Conjecture and Presentations of Simple Groups
\jour Algebra Logika
\yr 2005
\vol 44
\issue 4
\pages 399--437
\mathnet{http://mi.mathnet.ru/al124}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2188932}
\zmath{https://zbmath.org/?q=an:1104.20032}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 4
\pages 219--242
\crossref{https://doi.org/10.1007/s10469-005-0023-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-23944517237}


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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. Giang Le Thi, “The relative hyperbolicity of one-relator relative presentations”, J. Group Theory, 12:6 (2009), 949–959  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    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 Algebra, 216:3 (2012), 524–534  crossref  mathscinet  zmath  isi  elib  scopus
    6. 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  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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