Book Review
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MathSciNet review:
1567425
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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.
Roger Alperin, Locally compact groups acting on trees and property $T$, Monatsh. Math. 93 (1982), no. 4, 261–265. MR 666827, DOI 10.1007/BF01295226
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, DOI 10.1112/jlms/s2-31.1.55
Hyman Bass, Some remarks on group actions on trees, Comm. Algebra 4 (1976), no. 12, 1091–1126. MR 419616, DOI 10.1080/00927877608822154
Hyman Bass, Groups of integral representation type, Pacific J. Math. 86 (1980), no. 1, 15–51. MR 586867
P. Cartier, Harmonic analysis on trees, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 419–424. MR 0338272
I. M. Chiswell, Abstract length functions in groups, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 3, 451–463. MR 427480, DOI 10.1017/S0305004100053093
I. M. Chiswell, The Bass-Serre theorem revisited, J. Pure Appl. Algebra 15 (1979), no. 2, 117–123. MR 535180, DOI 10.1016/0022-4049(79)90028-8
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, DOI 10.2307/2006973
9. M. J. Dunwoody, Countable groups with more than one end, preprint, 1982.
M. J. Dunwoody, Accessibility and groups of cohomological dimension one, Proc. London Math. Soc. (3) 38 (1979), no. 2, 193–215. MR 531159, DOI 10.1112/plms/s3-38.2.193
Beno Eckmann and Heinz Müller, Poincaré duality groups of dimension two, Comment. Math. Helv. 55 (1980), no. 4, 510–520. MR 604709, DOI 10.1007/BF02566702
Lothar Gerritzen and Marius van der Put, Schottky groups and Mumford curves, Lecture Notes in Mathematics, vol. 817, Springer, Berlin, 1980. MR 590243
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
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.
Roger C. Lyndon, Length functions in groups, Math. Scand. 12 (1963), 209–234. MR 163947, DOI 10.7146/math.scand.a-10684
Heinz Müller, Decomposition theorems for group pairs, Math. Z. 176 (1981), no. 2, 223–246. MR 607963, DOI 10.1007/BF01261870
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
Jean-Pierre Serre, Le problème des groupes de congruence pour SL2, Ann. of Math. (2) 92 (1970), 489–527 (French). MR 272790, DOI 10.2307/1970630
Jean-Pierre Serre, Cohomologie des groupes discrets, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970) Ann. of Math. Studies, No. 70, Princeton Univ. Press, Princeton, N.J., 1971, pp. 77–169 (French). MR 0385006
Jean-Pierre Serre, Arbres, amalgames, $\textrm {SL}_{2}$, Astérisque, No. 46, Société Mathématique de France, Paris, 1977 (French). Avec un sommaire anglais; Rédigé avec la collaboration de Hyman Bass. MR 0476875
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.
John Stallings, Groups of cohomological dimension one, Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVIII, New York, 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 124–128. MR 0255689
Richard G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 585–610. MR 240177, DOI 10.1016/0021-8693(69)90030-1
G. Ananda Swarup, Relative version of a theorem of Stallings, J. Pure Appl. Algebra 11 (1977/78), no. 1-3, 75–82. MR 466326, DOI 10.1016/0022-4049(77)90042-1
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
J. Tits, On buildings and their applications, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 209–220. MR 0439945
J. Tits, A “theorem of Lie-Kolchin” for trees, Contributions to algebra (collection of papers dedicated to Ellis Kolchin), Academic Press, New York, 1977, pp. 377–388. MR 0578488
Marvin D. Tretkoff, A topological approach to the theory of groups acting on trees, J. Pure Appl. Algebra 16 (1980), no. 3, 323–333. MR 558496, DOI 10.1016/0022-4049(80)90037-7
Yasuo Watatani, Property T of Kazhdan implies property FA of Serre, Math. Japon. 27 (1982), no. 1, 97–103. MR 649023
- 1.
- R. C. Alperin, Locally compact groups acting on trees and property T, Monatsh. Math. 93 (1982), 261-265. MR 0666827
- 2.
- R. C. Alperin and K. N. Moss, Complete trees for groups with a real valued length function, preprint, 1981. MR 810562
- 3.
- H. Bass, Some remarks on group actions on trees, Comm. Algebra 4 (1976), 1091-1126. MR 419616
- 4.
- H. Bass, Groups of integral representation type, Pacific J. Math. 86 (1980), 15-52. 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), 117-123. MR 535180
- 8.
- M. Culler and P. B. Shalen, Varieties of group representations and splittings of 3-manifolds, Ann. of Math. (2) (to appear). MR 683804
- 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. 38 (1979), 193-215. MR 531159
- 11.
- B. Eckmann and H. Müller, Poincaré duality groups of dimension two, Comment. Math. Helv. 55 (1980), 510-520. MR 604709
- 12.
- L. Gerritzen and M. van der Put, Schottky groups and Mumford curves, Lecture Notes in Math., vol. 817, Springer-Verlag, Berlin and New York, 1980. MR 590243
- 13.
- D. R. Grayson, Finite generation of K-groups of a curve over a finite field (after Daniel Quillen), Lecture Notes in Math. (to appear). MR 689367
- 14.
- J.-C. Hausmann, Sur l'usuge de critères pour reconnaître un groupe libre, un produit amalgamé ou une HNN-extension, L'Enseignement Math. 27 (1981), 221-242. 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.
- H. Müller, Decomposition theorems for group pairs, Math. Z. 176 (1981), 223-246. MR 607963
- 18.
- P. Scott and T. Wall, Topological methods in group theory, Homological Group Theory, LMS Lecture Notes 36, Cambridge Univ. Press, Cambridge, 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, LMS Lecture Notes 36, Cambridge Univ. Press, Cambridge, 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, Proc. Internat. Congr. Math. (Helsinki, 1978), vol. I, Acad. Sci. Fenn. Helsinki, 1980, pp. 57-63. MR 562596
- 28.
- J. Tits, On buildings and their applications, Proc. Internat. Congr. Math. (Vancouver, 1974), vol. I, 1974, pp. 209-220. MR 439945
- 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
- 30.
- M. D. Tretkoff, A topological approach to the theory of groups acting on trees, J. Pure Appl. Algebra 16 (1980), 323-333. MR 558496
- 31.
- Y. Watatani, Property T of Kazhdan implies property FA of Serre, Math. Japan 27 (1982), 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