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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Infinite general linear groups over rings


Author: George Maxwell
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0263932-9
Keywords: Infinite linear groups, normal subgroup, elementary automorphism
Article copyright: © Copyright 1970 American Mathematical Society