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Standard commutator formula

  • To the 100th Anniversary of Birthday of Dmitrii Konstantinovich Faddeev
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Abstract

Let R be a commutative ring with 1, A, B ⊴ R be its ideals, GL(n, R, A) be the principal congruence subgroup of level A in GL(n, A), and E(n, R, A) be the relative elementary subgroup of level A. We prove the following commutator formula

$$ [E(n,R,A),GL(n,R,B)] = [E(n,R,A),E(n,R,B)], $$

which generalizes known results. The proof is yet another variation on the theme of decomposition of unipotents.

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Authors
  1. N. A. Vavilov
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  2. A. V. Stepanov
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Additional information

Original Russian Text © N.A. Vavilov, A.V. Stepanov, 2008, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1, Matematika, Mekhanika, Astronomiya, 2008, No. 1, pp. 9–14.

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Vavilov, N.A., Stepanov, A.V. Standard commutator formula. Vestnik St.Petersb. Univ.Math. 41, 5–8 (2008). https://doi.org/10.3103/S1063454108010020

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  • DOI: https://doi.org/10.3103/S1063454108010020

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