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K1-theory and the congruence problem

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Abstract

The following results are presented: a) A K1-functor of a noncommutative ring with unity is a factor of a general linear group with respect to the subgroup of elementary matrices; b) a description is given of all the subgroups of finite index in a special linear group over the order in a field.

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Literature cited

  1. H. Bass, “K-theory and stable algebra,” Publ. Math.,22, 5–60 (1964).

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  2. H. Bass, J. Milnor, and J. P. Serre, “Solution of the congruence subgroup problem for SLn (n ⩾ 3) and Sp2n (n ⩾ 2),” Publ. Math.,33, 59–137 (1967).

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  3. H. Bass, “The stable structure of quite general linear groups,” Bull. Amer. Math. Soc.,70, 429–433 (1964).

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Authors and Affiliations

  1. Moscow Lomonosov State University, USSR

    L. N. Vasershtein

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  1. L. N. Vasershtein
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Translated from Matematicheskie Zametki, Vol. 5, No. 2, pp. 233–244, February, 1969.

This was proved by Serre for a commutative L.

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Vasershtein, L.N. K1-theory and the congruence problem. Mathematical Notes of the Academy of Sciences of the USSR 5, 141–148 (1969). https://doi.org/10.1007/BF01098314

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  • DOI: https://doi.org/10.1007/BF01098314

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