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Algebra Logika, 2003, Volume 42, Number 2, Pages 131–160 (Mi al22)  

This article is cited in 18 scientific papers (total in 18 papers)

A Generalization of Fibonacci Groups

V. G. Bardakov, A. Yu. Vesnin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We study the class of cyclically presented groups which contain Fibonacci groups and Sieradski groups. Conditions are specified for these groups to be finite, pairwise isomorphic, or aspherical. As a partial answer to the question of Cavicchioli, Hegenbarth, and Repov, it is stated that there exists a wide subclass of groups with an odd number of generators cannot appear as fundamental groups of hyperbolic three-dimensional manifolds of finite volume.

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English version:
Algebra and Logic, 2003, 42:2, 73–91

Bibliographic databases:

UDC: 512.817+515.162
Received: 12.02.2001

Citation: V. G. Bardakov, A. Yu. Vesnin, “A Generalization of Fibonacci Groups”, Algebra Logika, 42:2 (2003), 131–160; Algebra and Logic, 42:2 (2003), 73–91

Citation in format AMSBIB
\by V.~G.~Bardakov, A.~Yu.~Vesnin
\paper A Generalization of Fibonacci Groups
\jour Algebra Logika
\yr 2003
\vol 42
\issue 2
\pages 131--160
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 2
\pages 73--91

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    This publication is cited in the following articles:
    1. Mohamed E., Williams G., “An Investigation Into the Cyclically Presented Groups With Length Three Positive Relators”, Exp. Math.  crossref  isi  scopus
    2. Cavicchioli A, Repovs D, Spaggiari F, “Families of group presentations related to topology”, Journal of Algebra, 286:1 (2005), 41–56  crossref  mathscinet  zmath  isi
    3. Spaggiari F., “Asphericity of symmetric presentations”, Publicacions Matematiques, 50:1 (2006), 133–147  crossref  mathscinet  zmath  isi  elib  scopus
    4. Cavicchioli A., O'Brien E.A., Spaggiari F., “On some questions about a family of cyclically presented groups”, Journal of Algebra, 320:11 (2008), 4063–4072  crossref  mathscinet  zmath  isi  scopus
    5. Williams G., “The aspherical Cavicchioli-Hegenbarth-Repovs generalized Fibonacci groups”, Journal of Group Theory, 12:1 (2009), 139–149  crossref  mathscinet  zmath  isi  scopus
    6. Edjvet M., Williams G., “The cyclically presented groups with relators x(i) xi+k xi+l”, Groups Geometry and Dynamics, 4:4 (2010), 759–775  crossref  mathscinet  zmath  isi  scopus
    7. Telloni A.I., “Combinatorics of a class of groups with cyclic presentation”, Discrete Mathematics, 310:22 (2010), 3072–3079  crossref  mathscinet  zmath  isi  elib  scopus
    8. Williams G., “Unimodular Integer Circulants Associated with Trinomials”, International Journal of Number Theory, 6:4 (2010), 869–876  crossref  mathscinet  zmath  isi  scopus
    9. Williams G., “Groups of Fibonacci Type Revisited”, Int. J. Algebr. Comput., 22:8 (2012), 1240002  crossref  mathscinet  zmath  isi  elib  scopus
    10. Howie J., Williams G., “Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups”, J. Algebra, 371 (2012), 521–535  crossref  mathscinet  zmath  isi  elib  scopus
    11. Williams G., “Largeness and Sq-Universality of Cyclically Presented Groups”, Int. J. Algebr. Comput., 22:4 (2012), 1250035  crossref  mathscinet  zmath  isi  scopus
    12. Williams G., “Fibonacci Type Semigroups”, Algebr. Colloq., 21:4 (2014), 647–652  crossref  mathscinet  zmath  isi  scopus
    13. Bogley W.A., “on Shift Dynamics For Cyclically Presented Groups”, J. Algebra, 418 (2014), 154–173  crossref  mathscinet  zmath  isi  scopus
    14. Bogley W.A., Williams G., “Coherence, Subgroup Separability, and Metacyclic Structures For a Class of Cyclically Presented Groups”, J. Algebra, 480 (2017), 266–297  crossref  mathscinet  zmath  isi
    15. Howie J., Williams G., “Fibonacci Type Presentations and 3-Manifolds”, Topology Appl., 215 (2017), 24–34  crossref  mathscinet  zmath  isi  scopus
    16. A. Yu. Vesnin, T. A. Kozlovskaya, “Brieskorn manifolds, generated Sieradski groups, and coverings of lens space”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S175–S185  mathnet  crossref  crossref  isi  elib
    17. Motegi K., Teragaito M., “Generalized Torsion Elements and Bi-Orderability of 3-Manifold Groups”, Can. Math. Bul.-Bul. Can. Math., 60:4 (2017), 830–844  crossref  mathscinet  zmath  isi  scopus
    18. Mohamed E., Williams G., “Isomorphism Theorems For Classes of Cyclically Presented Groups”, Int. J. Algebr. Comput., 29:6 (2019), 1009–1017  crossref  mathscinet  zmath  isi  scopus
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