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Generators and relations for classical groups

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Geometry and Differential Geometry

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§4. References

  1. J. AHRENS, A. DRESS, and H. WOLFF, Relationen zwischen Symmetrien in orthogonalen Gruppen, J. reine angew. Math. 234 (1969) 1–11.

    MathSciNet  MATH  Google Scholar 

  2. F. BACHMANN, Aufbau der Geometrie aus dem Spiegelungsbegriff, 2nd edition, Springer-Verlag, New York-Heidelberg-Berlin, 1973.

    Book  MATH  Google Scholar 

  3. S. BECKEN, Spiegelungsrelationen in orthogonalen Gruppen, J. reine angew. Math. 210 (1962) 205–215.

    MathSciNet  MATH  Google Scholar 

  4. S. BÖGE née BECKEN, Definierende Relationen zwischen Erzeugenden der klassischen Gruppen, Abh. Math. Sem. Univ. Hamburg 30 (1967) 165–178.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. DIEUDONNÉ, La géométrie des groupes classiques, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955.

    MATH  Google Scholar 

  6. E.W. ELLERS, Relations in Classical Groups, J. Algebra 51 (1978) 19–24.

    Article  MathSciNet  MATH  Google Scholar 

  7. _____, Radical Relations in Unitary, Symplectic, and Orthogonal Groups, J. reine angew. Math. 306 (1979) 1–6.

    MathSciNet  MATH  Google Scholar 

  8. _____, Relations in Hyperreflection Groups, Proc. Amer. Math. Soc. (to appear).

    Google Scholar 

  9. _____, Defining Relations for the Equiaffine Group, Geometriae Dedicata (to appear).

    Google Scholar 

  10. _____, Relations in the Projective General Linear Group and in the Affine Subgroup (to appear).

    Google Scholar 

  11. _____ and W. NOLTE, Radical Relations in Orthogonal Groups (to appear).

    Google Scholar 

  12. M. GÖTZKY, Unverkürzbare Produkte und Relationen in unitären Gruppen, Math. Z. 104 (1968) 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  13. S.M. GREEN, Generators and Relations for the Special Linear Group over a Division Ring, Proc. Amer. Math. Soc. 62 (1977) 229–232.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. GÃœNTHER and W. NOLTE, Defining Relations in Orthogonal Groups of Characteristic Two, Canadian J. Math. (to appear).

    Google Scholar 

  15. K. MEYER, Transvektionsrelationen in metrischen Vektorräumen der Charakteristik 2, J. reine angew. Math. 233 (1968) 189–199.

    MathSciNet  MATH  Google Scholar 

  16. W. NOLTE, Spiegelungsrelationen in den engeren orthogonalen Gruppen, J. reine angew. Math. 273 (1975) 150–152.

    MathSciNet  MATH  Google Scholar 

  17. _____, Das Relationenproblem für eine Klasse von Untergruppen orthogonaler Gruppen, J. reine angew. Math. 292 (1977) 211–220.

    MathSciNet  MATH  Google Scholar 

  18. U. SPENGLER, Relationen zwischen symplektischen Transvektionen, J. reine angew. Math. 274/275 (1975) 141–149.

    MathSciNet  MATH  Google Scholar 

  19. G. THOMSEN, Grundlagen der Elementargeometrie in gruppen-algebraischer Behandlung, Hamburger Mathematische Einzelschriften, 16. Heft, B.G. Teubner-Verlag, Leipzig-Berlin, 1933.

    Google Scholar 

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Rafael Artzy Izu Vaisman

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© 1980 Springer-Verlag

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Ellers, E.W. (1980). Generators and relations for classical groups. In: Artzy, R., Vaisman, I. (eds) Geometry and Differential Geometry. Lecture Notes in Mathematics, vol 792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088659

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  • DOI: https://doi.org/10.1007/BFb0088659

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  • Print ISBN: 978-3-540-09976-5

  • Online ISBN: 978-3-540-39214-9

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