On normal subgroups of GL 2 over rings with many units

L. N. Vaserstein

Compositio Mathematica (1990)

  • Volume: 74, Issue: 2, page 157-164
  • ISSN: 0010-437X

How to cite

top

Vaserstein, L. N.. "On normal subgroups of $\mathrm {GL}_2$ over rings with many units." Compositio Mathematica 74.2 (1990): 157-164. <http://eudml.org/doc/90014>.

@article{Vaserstein1990,
author = {Vaserstein, L. N.},
journal = {Compositio Mathematica},
keywords = {normal subgroup problem; linear groups over rings; sandwich theorem; sum of units; stable range; Jacobson radical},
language = {eng},
number = {2},
pages = {157-164},
publisher = {Kluwer Academic Publishers},
title = {On normal subgroups of $\mathrm \{GL\}_2$ over rings with many units},
url = {http://eudml.org/doc/90014},
volume = {74},
year = {1990},
}

TY - JOUR
AU - Vaserstein, L. N.
TI - On normal subgroups of $\mathrm {GL}_2$ over rings with many units
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 74
IS - 2
SP - 157
EP - 164
LA - eng
KW - normal subgroup problem; linear groups over rings; sandwich theorem; sum of units; stable range; Jacobson radical
UR - http://eudml.org/doc/90014
ER -

References

top
  1. 1 E. Abe, Chevalley groups over local rings, Tôhoku Math. J.21 (1969), 474-494. Zbl0188.07201MR258837
  2. 2 J.-B. An and X.-P. Tang, The structure of symplectic groups over semilocal rings, Acta Math. Sinica (N.S.) 1:1 (1985), 1-15. Zbl0581.20046MR831027
  3. 3 H. Bass, K-theory and stable algebra, Publ. Math. IHES22 (1964), 5-60. Zbl0248.18025MR174604
  4. 4 D.L. Costa and G.E. Keller, On the normal subgroups of SL(2, A), J. Pure Appl. Alg.53:3 (1988), 201-227. Zbl0654.20051MR961360
  5. 5 C.N. Chang, The structure of the symplectic group over semi-local domains, J. Algebra35 (1975), 457-476. Zbl0326.20041MR369560
  6. 6 W. Klingenberg, Lineare Gruppen über lokalen Ringen, Amer. J. Math.83 (1961), 137-153. Zbl0098.02303MR124412
  7. 7 W. Klingenberg, Die Structur der linearen Gruppe über einen nichtkommutativeen lokalen Ring, Arch. Math.13 (1962), 73-81. Zbl0106.25203MR143817
  8. 8 L. Yu. Kolotilina and N.A. Vavilov, Normal structure of the full linear group over semilocal rings, J. Sov. Math.19:1 (1982), 998-999. Zbl0485.20045
  9. 9 N.H.J. Lacroix, Two-dimensional linear groups over local rings, Can. J. Math.21 (1969),106-135. Zbl0169.34404MR237658
  10. 10 N.H.J. Lacroix and C. Levesque, Sur les sous-groups normaux de SL 2 sur un anneau local, Can. Math. Bull.26:2 (1983), 209-219. Zbl0515.20032MR697803
  11. 11 B.A. Magurn, W. van der Kallen, and L.N. Vaserstein, Absolute stable rank and Witt cancellation for noncommutative rings, Inv. Math.91:3 (1988), 525-542. Zbl0639.16015MR928496
  12. 12 A.W. Mason, On GL2 of a local ring in which 2 is not a unit, Can. Math. Bull.30:2(1987), 165-176. Zbl0589.20032MR889534
  13. 13 B.R. McDonald, GL2 of rings with many units, Commun. Algebra8:9 (1980), 869-888. Zbl0436.20031MR571047
  14. 14 B.R. McDonald, Geometric algebra over local rings, New York-Basel, Marcel Dekker, 1976. Zbl0346.20027MR476639
  15. 15 P. Menal and L.N. Vaserstein, On subgroups of GL2 over Banach algebras and von Neumann regular rings which are normalized by elementary matrices, preprint, 20 p. Zbl0724.20034
  16. 16 H.H. Storrer, Epimorphic extensions of non-commutative rings, Comm. Math. Helv.18 (1973), 72-86. Zbl0258.16027MR321977
  17. 17 S. Tazhetdivon, Subnormal structure of two-dimensional linear groups over local rings, Alg. Logic22:6 (1983), 707-713. Zbl0542.20028MR781401
  18. 18 S. Tazhetdinov, Subnormal structure of two-dimensional linear groups over rings that are close to fields Alg. Logic24:4 (1985), 414-425. Zbl0587.20028MR830010
  19. 19 L.N. Vaserstein, K1-theory and the congruence subgroup problem, Mat. Zametki5 (1969), 233-244 = Math. Notes5 (1969), 141-148. Zbl0195.32202MR246941
  20. 20 L.N. Vaserstein, Normal subgroups of the general linear groups over von Neumann regular rings, Proc. Amer. Math. Soc.96:2 (1986), 209-214. Zbl0594.16007MR818445
  21. 21 L.N. Vaserstein, Normal subgroups of the general linear groups over Banach algebras, J.P.A. Algebra41 (1986), 99-112. Zbl0589.20030MR844468
  22. 22 L.N. Vaserstein, Subnormal structure of the general linear groups over Banach algebras, J. Pure Appl. Alg., 52 (1988), 187-195. Zbl0653.20050MR949349
  23. 23 L.N. Vaserstein, Bass's first stable range condition, J. Pure Appl. Algebra34:2-3 (1984), 319-330. Zbl0547.16017MR772066
  24. 24 L.N. Vaserstein, An answer to the question of M. Newman on matrix completion, Proc. Amer. Math. Soc.97:2 (1986), 189-196. Zbl0601.15011MR835863
  25. 25 L.N. Vaserstein, On stabilization for general linear groups over a ring, Mat. Sbornik79:3 (1969), 405-424 = Math. USSR Sbornik8, 383-400. Zbl0238.20057MR267009
  26. 26 L.Q. Wang and Y.Z. Zhang, GL2 over full rings, Chin. An. Math. ser. B, 8:4 (1987), 434-439. Zbl0638.20029MR925913

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.