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Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Author: Warren Dicks
Title: Groups, trees and projective modules
Additional book information: Lecture Notes in Math., vol. 790, Springer-Verlag, Berlin and New York, 1980, 126 pp., $9.80.

Author: Jean-Pierre Serre
Title: Trees
Additional book information: Springer-Verlag, Berlin and New York, 1980, ix + 142 pp., $29.80.

References [Enhancements On Off] (What's this?)

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  • 2. Roger C. Alperin and Kenneth N. Moss, Complete trees for groups with a real-valued length function, J. London Math. Soc. (2) 31 (1985), no. 1, 55–68. MR 810562, https://doi.org/10.1112/jlms/s2-31.1.55
  • 3. H. Bass, Some remarks on group actions on trees, Comm. Algebra 4 (1976), 1091-1126. MR 419616
  • 4. Hyman Bass, Groups of integral representation type, Pacific J. Math. 86 (1980), no. 1, 15–51. MR 586867
  • 5. P. Cartier, Harmonic analysis on trees, Proc. Sympos. Pure Math., vol. 26, Amer. Math. Soc., Providence, R. I., 1973, pp. 419-424. MR 338272
  • 6. I. M. Chiswell, Abstract length functions in groups, Math. Proc. Cambridge Philos. Soc. 80 (1976), 451-463. MR 427480
  • 7. I. M. Chiswell, The Bass-Serre theorem revisited, J. Pure Appl. Algebra 15 (1979), no. 2, 117–123. MR 535180, https://doi.org/10.1016/0022-4049(79)90028-8
  • 8. Marc Culler and Peter B. Shalen, Varieties of group representations and splittings of 3-manifolds, Ann. of Math. (2) 117 (1983), no. 1, 109–146. MR 683804, https://doi.org/10.2307/2006973
  • 9. M. J. Dunwoody, Countable groups with more than one end, preprint, 1982.
  • 10. M. J. Dunwoody, Accessibility and groups of cohomological dimension one, Proc. London Math. Soc. (3) 38 (1979), no. 2, 193–215. MR 531159, https://doi.org/10.1112/plms/s3-38.2.193
  • 11. Beno Eckmann and Heinz Müller, Poincaré duality groups of dimension two, Comment. Math. Helv. 55 (1980), no. 4, 510–520. MR 604709, https://doi.org/10.1007/BF02566702
  • 12. Lothar Gerritzen and Marius van der Put, Schottky groups and Mumford curves, Lecture Notes in Mathematics, vol. 817, Springer, Berlin, 1980. MR 590243
  • 13. Daniel R. Grayson, Finite generation of 𝐾-groups of a curve over a finite field (after Daniel Quillen), Algebraic 𝐾-theory, Part I (Oberwolfach, 1980) Lecture Notes in Math., vol. 966, Springer, Berlin-New York, 1982, pp. 69–90. MR 689367
  • 14. Jean-Claude Hausmann, Sur l’usage de critères pour reconnaître un groupe libre, un produit amalgamé ou une HNN-extension, Enseign. Math. (2) 27 (1981), no. 3-4, 221–242 (1982) (French). MR 659150
  • 15. P. A. Linnell, conversation with R. C. A. at Oberwolfach, July, 1982.
  • 16. R. C. Lyndon, Length functions in groups, Math. Scand. 12 (1963), 209-234. MR 163947
  • 17. Heinz Müller, Decomposition theorems for group pairs, Math. Z. 176 (1981), no. 2, 223–246. MR 607963, https://doi.org/10.1007/BF01261870
  • 18. Peter Scott and Terry Wall, Topological methods in group theory, Homological group theory (Proc. Sympos., Durham, 1977) London Math. Soc. Lecture Note Ser., vol. 36, Cambridge Univ. Press, Cambridge-New York, 1979, pp. 137–203. MR 564422
  • 19. J-P. Serre, Le problème des groupes de congruence pour SL2, Ann. of Math. (2) 92 (1970), 489-527. MR 272790
  • 20. J-P. Serre, Cohomologie des groupes discrete, Prospects in Mathematics, Ann. of Math. Studies, no. 70, Princeton Univ. Press, Princeton, N. J., 1971, pp. 77-169. MR 385006
  • 21. J-P. Serre, Arbres, amalgames, SL2, Astérisque Soc. Math. France 46 (1977). MR 476875
  • 22. J.-P. Serre, Arithmetic groups, Homological group theory (Proc. Sympos., Durham, 1977) London Math. Soc. Lecture Note Ser., vol. 36, Cambridge Univ. Press, Cambridge-New York, 1979, pp. 105–136. MR 564421
  • 23. P. B. Shalen, conversation with R.C.A. at Rice Univ., August, 1982.
  • 24. J. R. Stallings, Groups of cohomological dimension one, Proc. Sympos. Pure Math., vol. 17, Amer. Math. Soc., Providence, R. I., 1968, pp. 124-128. MR 255689
  • 25. R. G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 585-601. MR 240177
  • 26. G. A. Swarup, Relative version of a theorem of Stallings, J. Pure Appl. Algebra 11 (1977), 75-82. MR 466326
  • 27. J. Tits, The work of Gregori Aleksandrovitch Margulis, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, pp. 57–63. MR 562596
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  • 29. J. Tits, A "theorem of Lie-Kolchin" for trees, Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin, Academic Press, New York, 1977, pp. 377-388. MR 578488
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  • 31. Yasuo Watatani, Property T of Kazhdan implies property FA of Serre, Math. Japon. 27 (1982), no. 1, 97–103. MR 649023

Review Information:

Reviewer: Roger C. Alperin
Journal: Bull. Amer. Math. Soc. 8 (1983), 401-405
DOI: https://doi.org/10.1090/S0273-0979-1983-15146-7
American Mathematical Society