References[1] R. C., Alperin and K. N., Moss, Complete trees for groups with a real-valued length function, J. London Math. Soc. 31 (1985), 55–68.
[2] R., Baer, The subgroup of the elements of finite order of an abelian group, Ann. Math. 37 (1936), 766–781.
[3] S. A., Basarab, On a problem raised by Alperin and Bass. In: Arboreal Group Theory (ed. R. C., Alperin), MSRI Publications vol. 19, pp. 35–68, Springer-Verlag, New York, 1991.
[4] H., Bass, Group actions on non-archimedean trees. In: Arboreal Group Theory (ed. R. C., Alperin), MSRI Publications vol. 19, pp. 69–131, Springer-Verlag, New York, 1991.
[5] V. N., Berestovskii and C. P., Plaut, Covering ℝ-trees, ℝ-free groups, and dendrites, Adv. Math. 224 (2010), 1765–1783.
[6] M., Bestvina and M., Feighn, Stable actions of groups on real trees, Invent. Math. 121 (1995), 287–321.
[7] G., Cantor, Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, J. Reine Angew. Math. 77 (1874), 258–262. Also in: Georg Cantor, Gesammelte Abhandlungen (ed. E., Zermelo), Julius Springer, Berlin, 1932.
[8] G., Cantor, Über unendliche lineare Punktmannigfaltigkeiten V, Math. Ann. 21 (1883), 545–591.
[9] I. M., Chiswell, Harrison's theorem for Λ-trees, Quart. J. Math. Oxford (2) 45 (1994), 1–12.
[10] I. M., Chiswell, Introduction to Λ-Trees, World Scientific, Singapore, 2001.
[11] I. M., Chiswell, A-free groups and tree-free groups. In: Groups, Languages, Algorithms (ed. A.V., Borovik), Contemp. Math. vol. 378, pp. 79–86, Providence (RI), Amer. Math. Soc., 2005.
[12] I. M., Chiswell and T.W., Müller, Embedding theorems for tree-free groups, Math. Proc. Cambridge Philos. Soc. 149 (2010), 127–146.
[13] I. M., Chiswell, T.W., Müller, and J.-C., Schlage-Puchta, Compactness and local compactness for ℝ-trees, Arch. Math. 91 (2008), 372–378.
[14] D. E., Cohen, Combinatorial Group Theory: A Topological Approach, London Mathematical Society Student Texts vol. 14, Cambridge University Press, 1989.
[15] P. M., Cohn, Algebra (Second Edition), Volume 3, John Wiley & Sons, Chichester, 1991.
[16] M., Coornaert, T., Delzant, and A., Papadopoulos, Géeométrie et Théorie des Groupes, Lecture Notes in Mathematics vol. 1441, Springer, Berlin, 1990.
[17] M. J., Dunwoody, Groups acting on protrees, J. London Math. Soc. 56 (1997), 125–136.
[18] L., Fuchs, Abelian Groups, Pergamon Press, Oxford, 1960.
[19] D., Gaboriau, G., Levitt, and F., Paulin, Pseudogroups of isometries of ℝ and Rips' Theorem on free actions on ℝ-trees, Israel J. Math. 87 (1994), 403–428.
[20] E., Ghys and P., de la Harpe, Sur les Groupes Hyperboliques d'après Mikhael Gromov, Birkhäuser, Boston, 1990.
[21] D., Gildenhuys, O., Kharlampovich, and A. G., Myasnikov, CSA groups and separated free constructions, Bull. Austral. Math. Soc. 52 (1995), 63–84.
[22] L., Greenberg, Discrete groups of motions, Can. J. Math. 12 (1960), 414–425.
[23] M., Gromov, Hyperbolic groups. In: Essays in Group Theory (ed. S. M., Gersten), Mathematical Sciences Research Institute Publications vol. 8, pp. 75–263, Springer-Verlag, New York, 1987.
[24] N., Harrison, Real length functions in groups, Trans. Amer. Math. Soc. 174 (1972), 77–106.
[25] P. J., Higgins, Notes on Categories and Groupoids, Van Nostrand Reinhold, London-New York-Melbourne, 1971. (Reprinted with a new preface by the author: Repr. Theory Appl. Categ. 7 (2005), 1–178 (electronic).)
[26] W., Imrich, On metric properties of tree-like spaces. In: Beiträge zur Graphentheorie und deren Anwendungen (ed. Sektion MARÖK der Technischen Hochschule Ilmenau), pp. 129–156, Oberhof, 1977.
[27] A., Kertész, Einführung in die Transfinite Algebra, Birkhäuser Verlag, Basel–Stuttgart, 1975.
[28] F., Levi, Arithmetische Gesetze im Gebiete diskreter Gruppen, Rend. Palermo 35 (1913), 225–236.
[29] G., Levitt, Constructing free actions on ℝ-trees, Duke Math. J. 69 (1993), 615–633.
[30] R. C., Lyndon and P. E., Schupp, Combinatorial Group Theory, Springer-Verlag, Berlin–Heidelberg, 1977.
[31] W., Magnus, A., Karrass, and D., Solitar, Combinatorial Group Theory. Presentations of Groups in Terms of Generators and Relations, reprint of the 1976 second edition, Dover, Mineola, NY, 2004.
[32] G. A., Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, Berlin–Heidelberg, 1991.
[33] J. C., Mayer, J., Nikiel, and L. G., Oversteegen, Universal spaces for ℝ-trees, Trans. Amer. Math. Soc. 334 (1992), 411–432.
[34] J.W., Morgan and P. B., Shalen, Valuations, trees and degenerations of hyperbolic structures: I, Ann. of Math. (2) 122 (1985), 398–476.
[35] J.W., Morgan and P. B., Shalen, Free actions of surface groups on ℝ-trees, Topology 30 (1991), 143–154.
[36] T.W., Müller, A hyperbolicity criterion for subgroups of RJ(G), Abh. Math. Semin. Univ. Hambg. 80 (2010), 193–205.
[37] T.W., Müller, Some contributions to the theory of RJ-groups. In preparation.
[38] T.W., Müller and J.-C., Schlage-Puchta, On a new construction in group theory, Abh. Math. Semin. Univ. Hambg. 79 (2009), 193–227.
[39] A. G., Myasnikov and V. N., Remeslennikov, Exponential groups, II: extensions of centralizers and tensor completion of CSA-groups, Internat. J. Algebra Comput. 6 (1996), 687–711.
[40] A. G., Myasnikov, V. N., Remeslennikov, and D., Serbin, Regular free length functions on Lyndon's free ℤ[t]-group Fℤ[t]. In: Groups, Languages, Algorithms (ed. A. V., Borovik), Contemp. Math. vol. 378, pp. 33–77, Providence (RI), Amer. Math. Soc., 2005.
[41] M. H. A., Newman, On theories with a combinatorial definition of “equivalence“, Ann. of Math. (2) 43 (1942) 223–243.
[42] F. S., Rimlinger, ℝ-trees and normalisation of pseudogroups, Exper. Math. 1 (1992), 95–114.
[43] H. L., Royden, Real Analysis, Macmillan, New York, 1963.
[44] H., Schubert, Categories, Springer-Verlag, Berlin–Heidelberg, 1972.
[45] J.-P., Serre, Trees, Springer-Verlag, Berlin–Heidelberg, 1980.
[46] H., Short, Notes on word hyperbolic groups. In: Group Theory from a Geometrical Viewpoint (eds. E., Ghys, A., Haefliger, and A., Verjovsky), World Scientific, Singapore, 1991.
[47] W., Sierpiński, Cardinal And Ordinal Numbers, Monographs of the Polish Academy of Science vol. 34, Warsaw, 1958.
[48] H. J. S., Smith, On the integration of discontinuous functions, Proc. London Math. Soc. 6 (1875), 140–153.
[49] T., Szele, Ein Analogon der Körpertheorie für abelsche Gruppen, J. Reine Angew. Math. 188 (1950), 167–192.
[50] J., Tits, A ‘theorem of Lie–Kolchin’ for trees. In: Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin, Academic Press, New York, 1977.
[51] M., Urbański and L. Q., Zamboni, On free actions on Λ-trees, Math. Proc. Camb. Phil. Soc. 113 (1993), 535–542.
[52] M. J., Wicks, Commutators in free products, J. London Math. Soc. 37 (1962), 433–444.
[53] M. J., Wicks, A general solution of binary homogeneous equations over free groups, Pacific J. Math. 41 (1972), 543–561.
[54] D. L., Wilkens, Group actions on trees and length functions, Michigan Math. J. 35 (1988), 141–150.
[55] A., Zastrow, Construction of an infinitely generated group that is not a free product of surface groups and abelian groups, but which acts freely on an ℝ-tree, Proc. Royal Soc. Edinburgh (A) 128 (1998), 433–445.