Characterization of dilatations which are expressible as a product of three transvections or three reflections
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- by Dragomir Ž. Đoković PDF
- Proc. Amer. Math. Soc. 92 (1984), 315-319 Request permission
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.References
- O. T. O’Meara, Lectures on linear groups, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 22, American Mathematical Society, Providence, R.I., 1974. Expository Lectures from the CBMS Regional Conference held at Arizona State University, Tempe, Ariz., March 26–30, 1973. MR 0349862
- B. B. Phadke, Products of transvections, Canadian J. Math. 26 (1974), 1412–1417. MR 447425, DOI 10.4153/CJM-1974-135-0
- B. B. Phadke, Products of reflections, Arch. Math. (Basel) 26 (1975), no. 6, 663–665. MR 396782, DOI 10.1007/BF01229796
Additional Information
- © Copyright 1984 American Mathematical Society
- 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