Normal subgroups in limit groups of prime index
-
Thomas S. Weigel
und
Jhoel S. Gutierrez
Abstract
Motivated by their study of pro-p limit groups,
D. H. Kochloukova and P. A. Zalesskii formulated in [15, Remark after Theorem 3.3]
a question concerning the minimum number of generators
Funding statement: The second author was supported by CNPq-Brazil.
Acknowledgements
The authors would like to thank H. Wilton for a very useful comment concerning an earlier version of the paper, and also the referee for his/her helpful remarks.
References
[1]
E. Alibegović and M. Bestvina,
Limit groups are
[2] B. Baumslag, Residually free groups, Proc. Lond. Math. Soc. (3) 17 (1967), 402–418. 10.1112/plms/s3-17.3.402Suche in Google Scholar
[3] M. Bestvina and M. Feighn, Notes on Sela’s work: Limit groups and Makanin–Razborov diagrams, Geometric and Cohomological Methods in Group Theory, London Math. Soc. Lecture Note Ser. 358, Cambridge University Press, Cambridge (2009), 1–29. 10.1017/CBO9781139107099.002Suche in Google Scholar
[4] T. Camps, V. Große Rebel and G. Rosenberger, Einführung in die kombinatorische und die geometrische Gruppentheorie, Berliner Studienreihe Math. 19, Heldermann, Lemgo, 2008. Suche in Google Scholar
[5] C. Champetier and V. Guirardel, Limit groups as limits of free groups, Israel J. Math. 146 (2005), 1–75. 10.1007/BF02773526Suche in Google Scholar
[6] B. Fine, A. M. Gaglione, A. Myasnikov, G. Rosenberger and D. Spellman, A classification of fully residually free groups of rank three or less, J. Algebra 200 (1998), no. 2, 571–605. 10.1006/jabr.1997.7205Suche in Google Scholar
[7] B. Fine, G. Rosenberger and M. Stille, Conjugacy pinched and cyclically pinched one-relator groups, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 2, 207–227. 10.5209/rev_REMA.1997.v10.n2.17397Suche in Google Scholar
[8]
V. Guirardel,
Limit groups and groups acting freely on
[9] I. Kapovich, Subgroup properties of fully residually free groups, Trans. Amer. Math. Soc. 354 (2002), no. 1, 335–362. 10.1090/S0002-9947-01-02840-9Suche in Google Scholar
[10] O. Kharlampovich and A. Myasnikov, Irreducible affine varieties over a free group. I. Irreducibility of quadratic equations and Nullstellensatz, J. Algebra 200 (1998), no. 2, 472–516. 10.1006/jabr.1997.7183Suche in Google Scholar
[11] O. Kharlampovich and A. Myasnikov, Irreducible affine varieties over a free group. II. Systems in triangular quasi-quadratic form and description of residually free groups, J. Algebra 200 (1998), no. 2, 517–570. 10.1006/jabr.1997.7184Suche in Google Scholar
[12] O. Kharlampovich and A. Myasnikov, Elementary theory of free non-abelian groups, J. Algebra 302 (2006), no. 2, 451–552. 10.1016/j.jalgebra.2006.03.033Suche in Google Scholar
[13] O. G. Kharlampovich, A. G. Myasnikov, V. N. Remeslennikov and D. E. Serbin, Subgroups of fully residually free groups: Algorithmic problems, Group Theory, Statistics, and Cryptography, Contemp. Math. 360, American Mathematical Society, Providence (2004), 63–101. 10.1090/conm/360/06571Suche in Google Scholar
[14]
D. H. Kochloukova,
On subdirect products of type
[15] D. Kochloukova and P. Zalesskii, Subgroups and homology of extensions of centralizers of pro-p groups, Math. Nachr. 288 (2015), no. 5–6, 604–618. 10.1002/mana.201400104Suche in Google Scholar
[16] F. Paulin, Sur la théorie élémentaire des groupes libres (d’après Sela), Astérisque (2004), no. 294, 363–402. Suche in Google Scholar
[17] Z. Sela, Diophantine geometry over groups. I. Makanin–Razborov diagrams, Publ. Math. Inst. Hautes Études Sci. (2001), no. 93, 31–105. 10.1007/s10240-001-8188-ySuche in Google Scholar
[18] Z. Sela, Diophantine geometry over groups. II. Completions, closures and formal solutions, Israel J. Math. 134 (2003), 173–254. 10.1007/BF02787407Suche in Google Scholar
[19] J.-P. Serre, Galois Cohomology, Springer Monogr. Math., Springer, Berlin, 2002. Suche in Google Scholar
[20] J.-P. Serre, Trees, Springer Monogr. Math., Springer, Berlin, 2003. Suche in Google Scholar
[21] H. Wilton, Abelianization of limit groups, 2015, http://mathoverflow.net/questions/209853/abelianization-of-limit-groups. Suche in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block
- Sandwich classification for GLn(R), O2n(R) and U2n(R,Λ) revisited
- Critical maximal subgroups and conjugacy of supplements in finite soluble groups
- Finite $\smash{p}$\hbox{-}groups of conjugate type {1,p3}
- Normal subgroups in limit groups of prime index
- Uncountable locally free groups and their group rings
- Full box spaces of free groups
- Almost congruence extension property for subgroups of free groups
- Solving equations of length seven over torsion-free groups
- On the structure of virtually nilpotent compact p-adic analytic groups
Artikel in diesem Heft
- Frontmatter
- Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block
- Sandwich classification for GLn(R), O2n(R) and U2n(R,Λ) revisited
- Critical maximal subgroups and conjugacy of supplements in finite soluble groups
- Finite $\smash{p}$\hbox{-}groups of conjugate type {1,p3}
- Normal subgroups in limit groups of prime index
- Uncountable locally free groups and their group rings
- Full box spaces of free groups
- Almost congruence extension property for subgroups of free groups
- Solving equations of length seven over torsion-free groups
- On the structure of virtually nilpotent compact p-adic analytic groups
