Infinite general linear groups over rings
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- by George Maxwell PDF
- Trans. Amer. Math. Soc. 151 (1970), 371-375 Request permission
Abstract:
We are interested in the normal subgroups of the group G of automorphisms of a free module of infinite type over a commutative ring A. To this end, we introduce a certain “elementary” subgroup E of G and find that the subgroups of G normalised by E are exactly those which lie in congruence layers determined by the ideals of A. The normal subgroups are thus to be found in such layers.References
- H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 5–60. MR 174604
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
- Alex Rosenberg, The structure of the infinite general linear group, Ann. of Math. (2) 68 (1958), 278–294. MR 102528, DOI 10.2307/1970248
- W. R. Scott, Group theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0167513
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 151 (1970), 371-375
- MSC: Primary 20.75
- DOI: https://doi.org/10.1090/S0002-9947-1970-0263932-9
- MathSciNet review: 0263932