Dimension theory and nonstable K -theory for net groups

Anthony Bak; Alexei Stepanov

Rendiconti del Seminario Matematico della Università di Padova (2001)

  • Volume: 106, page 207-253
  • ISSN: 0041-8994

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Bak, Anthony, and Stepanov, Alexei. "Dimension theory and nonstable $K$-theory for net groups." Rendiconti del Seminario Matematico della Università di Padova 106 (2001): 207-253. <http://eudml.org/doc/108564>.

@article{Bak2001,
author = {Bak, Anthony, Stepanov, Alexei},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {207-253},
publisher = {Seminario Matematico of the University of Padua},
title = {Dimension theory and nonstable $K$-theory for net groups},
url = {http://eudml.org/doc/108564},
volume = {106},
year = {2001},
}

TY - JOUR
AU - Bak, Anthony
AU - Stepanov, Alexei
TI - Dimension theory and nonstable $K$-theory for net groups
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2001
PB - Seminario Matematico of the University of Padua
VL - 106
SP - 207
EP - 253
LA - eng
UR - http://eudml.org/doc/108564
ER -

References

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  2. [Bk2] A. Bak, K-theory of forms, Annals Math. Studies98, Princeton Univ. PressPrinceton, N.J.1981. Zbl0465.10013MR632404
  3. [Bk3] A. Bak, Finite completions, Unpublished. 
  4. [Bk4] A. Bak, Lectures on dimension theory, algebraic homotopy theory, and nonabelian K-theory, Lecture Notes, Buenos-Aires, 1995. 
  5. [Bk5] A. Bak, Dimension theory and group valued functors, preprint. 
  6. [BkV] A. Bak - N.A. Vavilov, Structure of hyperbolic unitary groups I. Elementary subgroups, Algebra Colloquium, 7:2 (2000), pp. 159-196. Zbl0963.20024MR1810843
  7. [BV1] Z.I. Borewicz - N.A. Vavilov, The distribution of subgroups containing a group of block diagonal matrices in the general linear group over a ring, Sov. Math. - Izv. VUZ, 26:11 (1982), pp. 13-18. Zbl0521.20033
  8. [BV1] Z.I. Borewich - - N.A. Vavilov, The distribution of subgroups in the general linear group over a commutative ring, Proc. Steklov. Inst. Math., 3 (1985), pp. 27-46. Zbl0653.20048
  9. [G] I.Z. Golubchik, On the subgroups of the general linear group GLn(R) over an associative ring, R. Russian Math. Surveys, 39:1 (1984), pp. 157-158. Zbl0572.20031MR733962
  10. [H] R. Hazrat, Dimension theory and nonstable K1 of quadratic modules, K-Theory, to appear. Zbl1020.19001MR1962906
  11. [M] J. Milnor, Introduction to algebraic K-theory, Annals Math. StudiesPrinceton Univ. PressPrinceton, N.J., 1971. Zbl0237.18005MR349811
  12. [Mu] A. Mundkur, Dimension theory and nonstable K1, Algebras and Representation Theory, to appear. Zbl1010.19001MR1890592
  13. [S1] A.V. Stepanov, On the distribution of subgroups normalized by a given subgroup, J. Sov. Math., 64 (1993), pp. 769-776. Zbl0790.20069MR1164862
  14. [S2] A.V. Stepanov, Description of subgroups of the general linear group over a ring with the use of stability conditions, Rings and linear groups, Krasnodar Univ. Press, Krasnodar, Russian, 1988, 82-91. MR1206033
  15. [SuTu] A.A. Suslin - M.S. Tulenbaev, A theorem on stabilization for Milnor's K2-functor, J. Sov. Math., 17 (1981), pp. 1804-1819. Zbl0461.18008
  16. [T] G. Tang, Hermitian Groups and K-Theory, K-Theory, 13:3 (1998), pp. 209-267. Zbl0899.19003MR1609905
  17. [Tu] M.S. Tulenbaev, The Schur multiplier of the group of elementary matrices of finite order, J. Sov. Math., 17:4 (1981), pp. 2062-2067. Zbl0459.20042
  18. [Vs1] L.N. Vaserstein, On normal subgroups of GLn over a ring, Lecture Notes Math., 854 (1981), pp. 456-465. Zbl0464.20030MR618316
  19. [Vv1] N.A. Vavilov, Subgroups of the general linear group over a ring that contain a group of block-triangular matrices, Transl. Amer. Math. Soc., 2nd Ser., 132 (1986), pp. 103-104. Zbl0594.20040
  20. [Vv2] N.A. Vavilov, Structure of Chevalley groups over commutative rings, Proc. Conf. Non-associative algebras and related topics, Hiroshima, 1990World Sci. Publ. Singapore et al. (1991), 219-335. Zbl0799.20042MR1150262
  21. [VvS] N.A. Vavilov - A.V. Stepanov, Subgroups of the general linear group over rings satisfying stability conditions, Sov. Math., Izv. VUZ, 33:10 (1989), pp. 23-31. Zbl0702.20033MR1044472

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