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Residually finite groups. (English) Zbl 0196.04704

Keywords:
group theory
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[1] E. Artin, Theorie der Zoepfe, Abh. Math. Sem. Univ. Hamburg 4 (1925), 47-72. · JFM 51.0450.01
[2] Benjamin Baumslag, Residually free groups, Proc. London Math. Soc. (3) 17 (1967), 402 – 418. · Zbl 0166.01502
[3] Gilbert Baumslag, A non-hopfian group, Bull. Amer. Math. Soc. 68 (1962), 196 – 198. · Zbl 0108.02701
[4] Gilbert Baumslag, On generalised free products, Math. Z. 78 (1962), 423 – 438. · Zbl 0104.24402
[5] Gilbert Baumslag, On the residual finiteness of generalised free products of nilpotent groups, Trans. Amer. Math. Soc. 106 (1963), 193 – 209. · Zbl 0112.25904
[6] Gilbert Baumslag, On the residual nilpotence of some varietal products, Trans. Amer. Math. Soc. 109 (1963), 357 – 365. · Zbl 0118.03501
[7] Gilbert Baumslag, Residual nilpotence and relations in free groups, J. Algebra 2 (1965), 271 – 282. · Zbl 0131.02201
[8] Gilbert Baumslag, Some groups that are just about free, Bull. Amer. Math. Soc. 73 (1967), 621 – 622. · Zbl 0153.35001
[9] Gilbert Baumslag, Residually finite one-relator groups, Bull. Amer. Math. Soc. 73 (1967), 618 – 620. · Zbl 0153.34904
[10] Gilbert Baumslag, Some theorems on the free groups of certain product varieties, J. Combinatorial Theory 2 (1967), 77 – 99. · Zbl 0237.20021
[11] Gilbert Baumslag, On the residual nilpotence of certain one-relator groups, Comm. Pure Appl. Math. 21 (1968), 491 – 506. · Zbl 0186.32101
[12] Gilbert Baumslag and Donald Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199 – 201. · Zbl 0108.02702
[13] William W. Boone, Certain simple, unsolvable problems of group theory. V, VI, Nederl. Akad. Wetensch. Proc. Ser. A. 60 = Indag. Math. 19 (1957), 22 – 27, 227 – 232. · Zbl 0067.25706
[14] K. Brauner, Zur Geometrie der Funktionen zweier komplexer Veraenderlicher, Abh. Math. Sem. Univ. Hamburg 6 (1928), 1-55. · JFM 54.0373.01
[15] J. L. Britton, The word problem for groups, Proc. London Math. Soc. (3) 8 (1958), 493 – 506. · Zbl 0092.00801
[16] Bruce Chandler, The representation of a generalized free product in an associative ring, Comm. Pure Appl. Math. 21 (1968), 271 – 288. · Zbl 0167.02201
[17] M. Dehn, Über unendliche diskontinuierliche Gruppen, Math. Ann. 71 (1911), no. 1, 116 – 144 (German). · JFM 42.0508.03
[18] M. Dehn, Transformation der Kurven auf zweiseitigen Flächen, Math. Ann. 72 (1912), no. 3, 413 – 421 (German). · JFM 43.0571.03
[19] Ralph H. Fox, On Fenchel’s conjecture about \?-groups, Mat. Tidsskr. B. 1952 (1952), 61 – 65. · Zbl 0049.15404
[20] Karen N. Frederick, The Hopfian property for a class of fundamental groups, Comm. Pure Appl. Math. 16 (1963), 1 – 8. · Zbl 0115.40503
[21] R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Funktionen., I, Teubner, Berlin, 1897, pp. 186-187. · JFM 28.0334.01
[22] K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29 – 62. · Zbl 0077.02901
[23] Karl Gruenberg, The residual nilpotence of certain presentations of finite groups, Arch. Math. (Basel) 13 (1962), 408 – 417. · Zbl 0111.02804
[24] Marshall Hall Jr., A topology for free groups and related groups, Ann. of Math. (2) 52 (1950), 127 – 139. · Zbl 0045.31204
[25] P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419 – 436. · Zbl 0056.25603
[26] P. Hall, On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595 – 622. · Zbl 0091.02501
[27] Graham Higman, A finitely related group with an isomorphic proper factor group, J. London Math. Soc. 26 (1951), 59 – 61. · Zbl 0042.02103
[28] Graham Higman, A finitely generated infinite simple group, J. London Math. Soc. 26 (1951), 61 – 64. · Zbl 0042.02201
[29] Graham Higman, A remark on finitely generated nilpotent groups, Proc. Amer. Math. Soc. 6 (1955), 284 – 285. · Zbl 0065.25804
[30] K. A. Hirsch, On infinite soluble groups. III, Proc. London Math. Soc. (2) 49 (1946), 184 – 194. · Zbl 0063.02021
[31] H. Hopf, Beiträge zur Klassifizierung der Flächenabbildungen, J. Reine Angew. Math. 165 (1931), 225-236. · JFM 57.0726.01
[32] Robert A. Katz and Wilhelm Magnus, Residual properties of free groups, Comm. Pure Appl. Math. 22 (1968), 1 – 13. · Zbl 0157.05202
[33] A. Learner, Residual properties of polycyclic groups, Illinois J. Math. 8 (1964), 536 – 542. · Zbl 0124.26304
[34] A. I. Lihtman, On residually nilpotent groups, Sibirsk. Mat. Ž. 6 (1965), 862 – 866 (Russian). · Zbl 0171.28403
[35] W. Magnus, Das Identitätsproblem für Gruppen mit einer definierenden Relation, Math. Ann. 106 (1932), no. 1, 295 – 307 (German). · JFM 58.0125.01
[36] Wilhelm Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), no. 1, 259 – 280 (German). · Zbl 0011.15201
[37] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Wiley, New York, 1966. · Zbl 0138.25604
[38] Wilhelm Magnus and Ada Peluso, On knot groups, Comm. Pure Appl. Math. 20 (1967), 749 – 770. · Zbl 0164.54102
[39] A. Malcev, On isomorphic matrix representations of infinite groups, Rec. Math. [Mat. Sbornik] N.S. 8 (50) (1940), 405 – 422 (Russian, with English summary). · JFM 66.0088.03
[40] J. C. C. McKinsey, The decision problem for some classes of sentences without quantifiers, J. Symbolic Logic 8 (1943), 61 – 76. · Zbl 0063.03864
[41] J. Mennicke, Eine Bemerkung über Fuchssche Gruppen, Invent. Math. 2 (1967), 301 – 305 (German). · Zbl 0166.29202
[42] S. Moran, Associative operations on groups. I, Proc. London Math. Soc. (3) 6 (1956), 581 – 596. · Zbl 0073.01202
[43] A. Włodzimierz Mostowski, On the decidability of some problems in special classes of groups, Fund. Math. 59 (1966), 123 – 135. · Zbl 0143.03701
[44] B. H. Neumann, Adjunction of elements to groups, J. London Math. Soc. 18 (1943), 4 – 11. · Zbl 0028.33902
[45] B. H. Neumann, Varieties of groups, Bull. Amer. Math. Soc. 73 (1967), 603 – 613. · Zbl 0149.26704
[46] Hanna Neumann, Varieties of groups, Springer-Verlag New York, Inc., New York, 1967. · Zbl 0251.20001
[47] P. S. Novikov, On the algorithmic insolvability of the word problem in group theory, American Mathematical Society Translations, Ser 2, Vol. 9, American Mathematical Society, Providence, R. I., 1958, pp. 1 – 122. · Zbl 0093.01304
[48] Ada Peluso, A residual property of free groups, Comm. Pure Appl. Math. 19 (1966), 435 – 437. · Zbl 0145.24604
[49] Derek J. S. Robinson, Residual properties of some classes of infinite soluble groups, Proc. London Math. Soc. (3) 18 (1968), 495 – 520. · Zbl 0157.05402
[50] K. Seksenbaev, On the theory of polycyclic groups, Algebra i Logika Sem. 4 (1965), no. 3, 79 – 83 (Russian).
[51] Jean-Pierre Serre, Cohomologie Galoisienne, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1964. · Zbl 0143.05901
[52] Peter Stebe, Residual finiteness of a class of knot groups, Comm. Pure Appl. Math. 21 (1968), 563 – 583. · Zbl 0157.05203
[53] Arthur Steinberg, On free nilpotent quotient groups, Math. Z. 85 (1964), 185 – 196. · Zbl 0119.26403
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