Finite presentability of Φn(G), GLn(ℤG) and their elementary subgroups and Steinberg groups

Proceedings of the London Mathematical Society

Volumn 73, Issue 3, 1996, Pages 575-622

  Kiralis, Geoffrey ^a   Krstić, Sava ^b   McCool, James ^c  

^a Department of Obstetrics Gynecology   (United States)

^b TUFTS UNIVERSITY   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001653416     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/plms/s3-73.3.575     Document Type: Article

References (40)

1. H. BASS, Algebraic K-theory (Benjamin, New York, 1968).
2. H. BASS, A. HELLER, and R. SWAN, 'The Whitehead group of a polynomial extension', Inst. Hautes Études Sci. Publ. Math. 22 (1964) 61-79.
3. K. S. BROWN, Cohomology of groups (Springer, New York, 1982).
4. D. J. COLLINS, 'Peak reduction and automorphisms of free groups and free products', Combinatorial group theory and topology (eds S. M. Gersten and J. R. Stallings), Annals of Mathematics Studies 111 (Princeton University Press, 1987), pp. 107-120.
5. G. DENK and W. METZLER, 'Nielsen reduction in free groups with operators', Fund. Math. 129 (1988) 181-197.
6. R. K. DENNIS, 'In search of new "homology" functors having a close relationship to K-theory', preprint, Cornell University, 1976; Addendum, preprint, Cornell University, 1977.
7. S. C. GELLER, 'On some new algebraic K-groups', J. Pure Appl. Algebra 11 (1977) 157-178.
8. S. M. GERSTEN, 'A presentation for the special automorphism group of a free group', J. Pure Appl. Algebra 33 (1984) 269-279.
9. A. J. HAHN, 'The finite presentability of linear groups', Classical groups and related topics (eds A. J. Hahn, D. G. James, and Z. Wan), Contemporary Mathematics 82 (American Mathematical Society, Providence, R.I., 1989), pp. 23-33.
10. A. J. HAHN and O. T. O'MEARA, The classical groups and K-theory, Grundlehren der Mathematik 291 (Springer, New York, 1989).
11. A. HATCHER, 'Homological stability for automorphism groups of free groups', Comment. Math. Helv. 70 (1995) 39-62.
12. A. HATCHER and J. WAGONER, Pseudo-isotopies of compact manifolds, Astérisque 6 (Société Mathématique de France, Paris, 1973).
13. 3(II) obstruction to pseudoisotopy', thesis, Princeton University, 1978.
14. S. KALAJDŽIEVSKI, 'Automorphism group of a free group: centralizers and stabilizers', J. Algebra 150 (1992) 435-502.
15. S. KALAJDŽIEVSKI, 'Topographs and groups', J. Pure Appl. Algebra 80 (1992) 45-57.
16. 2', Lecture Notes in Mathematics 551 (Springer, New York, 1976), pp. 77-154.
17. J. KIRALIS, 'Non-abelian K-theory and pseudo-isotopies of 3-manifolds', K-theory, to appear.
18. S. KRSTIĆ, 'Finitely generated virtually free groups have finitely presented automorphism group', Proc. London Math. Soc. (3) 64 (1992) 49-69.
19. S. KRSTIĆ and J. MCCOOL, 'The non-finite presentability of the automorphism group of the free ℤ-group of rank 2', J. London Math. Soc., to appear.
20. A. O. KUKU, 'Some finiteness results in the higher K-theory of orders and group-rings', Topology Appl. 25 (1987) 185-191.
21. LI FUAN, 'Finite presentability of Steinberg groups over group rings', Acta Math. Sinica 5 (1989) 297-301.
22. J. L. LODAY, 'K-théorie algébrique et représentations de groupes', Ann. Sci. École Norm. Sup. (4) 9 (1976) 309-377.
23. 2', Lecture Notes in Mathematics 557 (Springer, New York, 1976), pp. 155-163.
24. W. MAGNUS, 'Über n-dimensionale Gittertransformationen', Acta Math. 64 (1935) 353-367.
25. W. MAGNUS, A. KARRASS, and D. SOLITAR, Combinatorial group theory (Interscience, New York, 1966).
26. J. MCCOOL, 'A presentation of the automorphism group of a free group of finite rank', J. London Math. Soc. (2) 8 (1974) 259-266.
27. J. MCCOOL, 'On Nielsen's presentation of the automorphism group of a free group', J. London Math. Soc. (2) 10 (1975) 265-270.
28. J. MCCOOL, 'Some remarks on IA automorphisms of free groups', Canad. J. Math. 40 (1988) 1144-1155.
29. J. MCCOOL, 'Automorphisms of finitely generated free G-groups', J. Algebra 166 (1994) 158-180.
30. C. MILLER, 'The second homology group of a group; relations among commutators', Proc. Amer. Math. Soc. 3 (1952) 588-595.
31. J. MILNOR, 'Whitehead torsion', Bull. Amer. Math. Soc. 72 (1966) 358-426.
32. J. MILNOR, Introduction to algebraic K-theory (Princeton University Press, 1971).
33. D. QUILLEN, 'Higher algebraic K-theory: I', Lecture Notes in Mathematics 341 (Springer, New York, 1973), pp. 85-147.
34. U. REHMANN and C. SOULÉ, 'Finitely presented groups of matrices', Lecture Notes in Mathematics 551 (Springer, New York, 1976), pp. 164-170.
35. A. A. SUSLIN, 'On the structure of the special linear group over polynomial rings', Math. USSR-Izv. 11 (1977) 221-238.
36. 2-functor', Rings and modules, J. Soviet Math. 17 (1981) 1804-1819.
37. L. N. VASERSTEIN, 'The stabilization for classical groups over rings', Math. USSR-Sb. 22 (1974) 271-303.
38. L. N. VASERSTEIN and A. A. SUSLIN, 'Serre's problem on projective modules over polynomial rings, and algebraic K-theory', Math. USSR-Izv. 10 (1976) 937-1001.
39. F. WALDHAUSEN, 'Algebraic K-theory of generalized free products, Parts I, II', Ann. of Math. 108 (1978) 135-204, 205-256.
40. F. WALDHAUSEN, 'Algebraic K-theory of topological spaces. II', Lecture Notes in Mathematics 763 (Springer, Berlin, 1979), pp. 356-394.