Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-30T20:42:22.607Z Has data issue: false hasContentIssue false
  • English
  • Français

The subnormal structure of general linear groups over rings

Published online by Cambridge University Press:  24 October 2008

L. N. Vaserstein
L. N. Vaserstein
Affiliation:
Department of Mathematics, The Pennsylvania State University, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

For any associative ring A with 1 and any integer n ≥ 1, let GLn A be the group of all invertible n × n matrices over A and EnA the subgroup generated by all elementary matrices aij, where a ∈ A and 1 ≤ i ≠ j ≤ n. When n = 1, the group GL1A is the multiplicative group of A and the group E1A is trivial.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 219 - 229
Copyright
Copyright © Cambridge Philosophical Society 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bak, A.. Subgroups of the general linear group normalized by relative elementary groups. In Algebraic K-theory, Lecture Notes in Math. vol. 967 (Springer-Verlag, 1980), pp. 1–22.Google Scholar
[2]Bass, H.. K-theory and stable algebra. Inst. Hautes Études Sci. Publ. Math. 22 (1964), 5–60.CrossRefGoogle Scholar
[3]Lennox, J. C. and Stonehewer, S. E.. Subnormal Subgroups of Groups (Clarendon Press, 1987).Google Scholar
[4]Li, Fu-An and Liu, Mulan. A generalized sandwich theorem. K-theory 1 (1987), 171–184.Google Scholar
[5]Gerasimov, V. N.. The unit group of free products. Mat. Sb. 134 (1987), 42–65.Google Scholar
[6]Lashinger, B.. Automorphismengruppen freier Moduln von unendlichen Rang. J. Algebra 122 (1989), 15–63.CrossRefGoogle Scholar
[7]Menal, P. and Vaserstein, L. N.. On subgroups of GL 2 over non-commutative local rings which are normalized by elementary matrices. Math. Ann. 285 (1989), 221–231.CrossRefGoogle Scholar
[8]Menal, P. and Vaserstein, L. N.. On the structure of GL 2 over stable range one rings. J. Algebra. (To appear.)Google Scholar
[9]Menal, P. and Vaserstein, L. N.. On subgroups of GL 2 over Banach algebras and von Neumann regular rings which are normalized by elementary matrices. J. Pure Appl. Algebra. (To appear.)Google Scholar
[10]Noskov, G. A.. The subnormal structure of the congruence subgroup of Merzlyakov. Sibirsk. Mat. Zh. 14 (1973), 680–683.Google Scholar
[11]Tazhetdinov, S.. Subnormal structure of symplectic groups over local rings. Mat. Zametki 37:2 (1985).Google Scholar
[12]Vaserstein, L. N.. On normal subgroups of GLn over a ring. In Algebraic K-theory, Lecture Notes in Math. vol. 854 (Springer-Verlag, 1981), pp. 456–465.Google Scholar
[13]Vaserstein, L. N.. Normal subgroups of the general linear groups over Banach algebras. J. Pure Appl. Algebra 41 (1986), 99–112.CrossRefGoogle Scholar
[14]Vaserstein, L. N.. Normal subgroups of the general linear groups over von Neumann regular rings. Proc. Amer. Math. Soc. 96 (1986), 209–214.CrossRefGoogle Scholar
[15]Vaserstein, L. N.. The subnormal structure of general linear groups. Math. Proc. Cambridge Philos. Soc. 99 (1986), 425–431.CrossRefGoogle Scholar
[16]Vaserstein, L. N.. The subnormal structure of the general linear groups over Banach algebras. J. Pure Appl. Algebra 52 (1988), 187–195.CrossRefGoogle Scholar
[17]Vavilov, N. A.. Subnormal structure of general linear group. Math. Proc. Cambridge Philos. Soc. 107 (1990). 193–196.CrossRefGoogle Scholar
[18]Wilson, J. S.. The normal and subnormal structure of general linear groups. Proc. Cambridge Philos. Soc. 71 (1972), 163–177.CrossRefGoogle Scholar