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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus


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Online
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1435-4446
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Volume 21, Issue 3

Issues

Note on the residual finiteness of Artin groups

Rubén Blasco-García / Arye Juhász / Luis Paris
Published Online: 2018-01-26 | DOI: https://doi.org/10.1515/jgth-2017-0049

Abstract

Let A be an Artin group. A partition 𝒫 of the set of standard generators of A is called admissible if, for all X,Y𝒫, XY, there is at most one pair (s,t)X×Y which has a relation. An admissible partition 𝒫 determines a quotient Coxeter graph Γ/𝒫. We prove that, if Γ/𝒫 is either a forest or an even triangle free Coxeter graph and AX is residually finite for all X𝒫, then A is residually finite.

References

  • [1]

    R. Blasco-Garcia, C. Martinez-Perez and L. Paris, Poly-freeness of even Artin groups of FC type, Groups Geom. Dyn., to appear. Web of ScienceGoogle Scholar

  • [2]

    J. Boler and B. Evans, The free product of residually finite groups amalgamated along retracts is residually finite, Proc. Amer. Math. Soc. 37 (1973), 50–52. CrossrefGoogle Scholar

  • [3]

    J. Burillo and A. Martino, Quasi-potency and cyclic subgroup separability, J. Algebra 298 (2006), no. 1, 188–207. CrossrefGoogle Scholar

  • [4]

    R. Charney and M. W. Davis, The K(π,1)-problem for hyperplane complements associated to infinite reflection groups, J. Amer. Math. Soc. 8 (1995), no. 3, 597–627. Google Scholar

  • [5]

    R. Charney and D. Peifer, The K(π,1)-conjecture for the affine braid groups, Comment. Math. Helv. 78 (2003), no. 3, 584–600. Google Scholar

  • [6]

    A. M. Cohen and D. B. Wales, Linearity of Artin groups of finite type, Israel J. Math. 131 (2002), 101–123. CrossrefGoogle Scholar

  • [7]

    J. Crisp, Injective maps between Artin groups, Geometric Group Theory Down Under (Canberra 1996), de Gruyter, Berlin (1999), 119–137. Google Scholar

  • [8]

    F. Digne, On the linearity of Artin braid groups, J. Algebra 268 (2003), no. 1, 39–57. CrossrefGoogle Scholar

  • [9]

    E. Godelle, Morphismes injectifs entre groupes d’Artin–Tits, Algebr. Geom. Topol. 2 (2002), 519–536. CrossrefGoogle Scholar

  • [10]

    C. M. Gordon, Artin groups, 3-manifolds and coherence, Bol. Soc. Mat. Mexicana (3) 10 (2004), 193–198. Google Scholar

  • [11]

    K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62. Google Scholar

  • [12]

    S. J. Pride, On the residual finiteness and other properties of (relative) one-relator groups, Proc. Amer. Math. Soc. 136 (2008), no. 2, 377–386. Google Scholar

  • [13]

    P. Przytycki and D. T. Wise, Graph manifolds with boundary are virtually special, J. Topol. 7 (2014), no. 2, 419–435. CrossrefWeb of ScienceGoogle Scholar

  • [14]

    H. Van der Lek, The homotopy type of complex hyperplane complements, Ph.D. thesis, Nijmegen, 1983. Google Scholar

About the article


Received: 2017-10-10

Revised: 2017-12-22

Published Online: 2018-01-26

Published in Print: 2018-05-01


The first named author was partially supported by Gobierno de Aragón, European Regional Development Funds, MTM2015-67781-P (MINECO/ FEDER) and by the Departamento de Industria e Innovación del Gobierno de Aragón and Fondo Social Europeo Phd grant.


Citation Information: Journal of Group Theory, Volume 21, Issue 3, Pages 531–537, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2017-0049.

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