LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Kopteva, Natalia; Williams, Gerald (2008)
Publisher: Oxford University Press
Languages: English
Types: Article
Subjects: QA

Classified by OpenAIRE into

arxiv: Mathematics::Group Theory
Pride groups, or 'groups given by presentations in which each defining relator involves at most two types of generators', include Coxeter groups, Artin groups, triangles of groups, and Vinberg's groups defined by periodic paired relations. We show that every non-spherical Pride group that is not a triangle of groups satisfies the Tits alternative.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] M. Bestvina, M. Feighn and M. Handel, The Tits alternative for Out(Fn). I. Dynamics of exponentially-growing automorphisms, Ann. of Math. (2) 151 (2000), no. 2, 517-623.
    • [2] M. Bestvina, M. Feighn and M. Handel, The Tits alternative for Out(Fn). II. A Kolchin type theorem, Ann. of Math. (2) 161 (2005), no. 1, 1-59.
    • [3] J. M. Corson, Amalgamated sums of groups, Proc. Edinburgh Math. Soc. (2) 39 (1996), no. 3, 561-570.
    • [4] M. Edjvet, G. Rosenberger, M. Stille and R. M. Thomas, On certain finite generalized tetrahedron groups, Computational and geometric aspects of modern algebra (Edinburgh, 1998), 54-65, London Math. Soc. Lecture Note Ser., 275, Cambridge Univ. Press, Cambridge, 2000.
    • [5] M. Gromov, Hyperbolic groups, Essays in group theory, 75-263, Math. Sci. Res. Inst. Publ., 8, Springer, New York, 1987.
    • [6] J. Howie and N. Kopteva, The Tits alternative for generalized tetrahedron groups, J. Group Theory, 9 (2006), no. 2, 173-189.
    • [7] N. V. Ivanov, Algebraic properties of the Teichmu¨ller modular group, (Russian) Dokl. Akad. Nauk SSSR 275 (1984), no. 4, 786-789.
    • [8] J. Meier, Geometric invariants for Artin groups, Proc. London Math. Soc. (3) 74 (1997), no. 1, 151-173.
    • [9] J. McCarthy, A “Tits-alternative” for subgroups of surface mapping class groups, Trans. Amer. Math. Soc. 291 (1985), no. 2, 583-612.
    • [10] G. Noskov and E. B. Vinberg, Strong Tits alternative for subgroups of Coxeter groups, J. Lie Theory 12 (2002), no. 1, 259-264.
    • [11] S. J. Pride, The (co)homology of groups given by presentations in which each defining relator involves at most two types of generators, J. Austral. Math. Soc. Ser. A 52 (1992), no. 2, 205- 218.
    • [12] M. Sageev and D. T. Wise, The Tits alternative for CAT(0) cubical complexes. Bull. London Math. Soc. 37 (2005), no. 5, 706-710.
    • [13] J. R. Stallings, Non-positively curved triangles of groups, Group Theory from a Geometrical Viewpoint (Trieste, 1990, ed. E. Ghys, A. Haefliger and P. de la Harpe), World Scientific, Singapore (1991), 491-503.
    • [14] J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972), 250-270.
    • [15] E. B. Vinberg, Groups defined by periodic paired relations, Sb. Math. 188 (1997), no. 9, 1269-1278.
    • [16] G. Williams, The Tits alternative for groups defined by periodic paired relations, Comm. Algebra 34 (2006), no. 1, 251-258.
    • Sobolev Institute of Mathematics, Acad. Koptyug ave., 4, Novosibirsk 630090, RUS-
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article