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Elementary Covering Numbers in Odd-Dimensional Unitary Groups

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Let (K, Δ) be a field of Hermitian forms and n ≥ 3. It is proved that if σ ∈ U2n+1(K, Δ) is a unitary matrix of level (K, Δ), then any short root transvection Tij(x) is a product of 4 elementary unitary conjugates of σ and σ−1. Moreover, the bound 4 is sharp. It is also shown that any extra short root transvection Ti(x, y) is a product of 12 elementary unitary conjugates of σ and σ−1. If the level of σ is (0,K × 0), then any (0,K × 0)-elementary extra short root transvection Ti(x, 0) is a product of 2 elementary unitary conjugates of σ and σ−1.

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Authors and Affiliations

  1. Chebyshev Laboratory, St.Petersburg State University, St.Petersburg, Russia

    R. Preusser

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  1. R. Preusser
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Correspondence to R. Preusser.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 500, 2021, pp. 158–176.

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Preusser, R. Elementary Covering Numbers in Odd-Dimensional Unitary Groups. J Math Sci 272, 450–463 (2023). https://doi.org/10.1007/s10958-023-06435-9

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  • DOI: https://doi.org/10.1007/s10958-023-06435-9

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