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

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

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
\Bibitem{BarVes03} \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 \mathnet{http://mi.mathnet.ru/al22} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2003626} \zmath{https://zbmath.org/?q=an:1031.57001} \transl \jour Algebra and Logic \yr 2003 \vol 42 \issue 2 \pages 73--91 \crossref{https://doi.org/10.1023/A:1023346206070} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-14644436785} 

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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. Mohamed E., Williams G., “An Investigation Into the Cyclically Presented Groups With Length Three Positive Relators”, Exp. Math.
2. Cavicchioli A, Repovs D, Spaggiari F, “Families of group presentations related to topology”, Journal of Algebra, 286:1 (2005), 41–56
3. Spaggiari F., “Asphericity of symmetric presentations”, Publicacions Matematiques, 50:1 (2006), 133–147
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
5. Williams G., “The aspherical Cavicchioli-Hegenbarth-Repovs generalized Fibonacci groups”, Journal of Group Theory, 12:1 (2009), 139–149
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
7. Telloni A.I., “Combinatorics of a class of groups with cyclic presentation”, Discrete Mathematics, 310:22 (2010), 3072–3079
8. Williams G., “Unimodular Integer Circulants Associated with Trinomials”, International Journal of Number Theory, 6:4 (2010), 869–876
9. Williams G., “Groups of Fibonacci Type Revisited”, Int. J. Algebr. Comput., 22:8 (2012), 1240002
10. Howie J., Williams G., “Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups”, J. Algebra, 371 (2012), 521–535
11. Williams G., “Largeness and Sq-Universality of Cyclically Presented Groups”, Int. J. Algebr. Comput., 22:4 (2012), 1250035
12. Williams G., “Fibonacci Type Semigroups”, Algebr. Colloq., 21:4 (2014), 647–652
13. Bogley W.A., “on Shift Dynamics For Cyclically Presented Groups”, J. Algebra, 418 (2014), 154–173
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
15. Howie J., Williams G., “Fibonacci Type Presentations and 3-Manifolds”, Topology Appl., 215 (2017), 24–34
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
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
18. Mohamed E., Williams G., “Isomorphism Theorems For Classes of Cyclically Presented Groups”, Int. J. Algebr. Comput., 29:6 (2019), 1009–1017
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