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Characterization of dilatations which are expressible as a product of three transvections or three reflections


Author: Dragomir Ž. Đoković
Journal: Proc. Amer. Math. Soc. 92 (1984), 315-319
MSC: Primary 15A23; Secondary 15A33, 20G99
DOI: https://doi.org/10.1090/S0002-9939-1984-0759641-5
MathSciNet review: 759641
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Abstract: Let $ V$ be a right vector space of dimension at least two over a division ring $ K$. We characterize the dilatations in $ {\text{GL}}(V)$ which are expressible as a product of three transvections; these are precisely those dilatations whose ratio is a commutator. Similarly, if char $ K \ne 2$, a dilatation is a product of three reflections if and only if its ratio is a negative of a commutator. The sufficiency of these conditions was established earlier by B. B. Phadke.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0759641-5
Keywords: Division ring, right vector space, dual space, general linear group
Article copyright: © Copyright 1984 American Mathematical Society

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