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On the dimensions of automorphism groups of four-dimensional double loops

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References

  1. Artzy, R.: Linear Geometry. Addison-Wesley, 3rd corr. ed., 1974

  2. Bödi, R.: On the Embedding of Zero-Dimensional Double Loops in Locally Euclidean Double Loops. Resultate der Math.22, 657–666 (1992)

    MATH  Google Scholar 

  3. Bödi, R.: Automorphism Groups of Locally Compact Connected Double Loops are Locally Compact. Arch. Math.61, 291–294 (1993)

    Article  MATH  Google Scholar 

  4. Bourbaki, N.: Lie groups and Lie algebras, Part I, Paris: Hermann 1975

    MATH  Google Scholar 

  5. Bredon, G.E.: Sheaf Theory. New York, 1967

  6. Bredon, G.E.: Generalized manifolds, revisited. Proc. Univ. of Georgia topology of manifolds institute, 1969, Athens, Georgia, p. 461–469, Chicago: Markham Publ. Comp. 1970

    Google Scholar 

  7. Chein, O., Pflugfelder, H.D., Smith, J.D.H. (eds.), Quasigroups and Loops: Theory and Applications. Berlin: Heldermann 1990

    Google Scholar 

  8. Dold, A.: Lectures on Algebraic Topology, Berlin Heidelberg New York: Springer 1972

    MATH  Google Scholar 

  9. Floyd, E.E.: On periodic maps and the Euler characteristic of associated spaces. Trans. Am. Math. Soc.72, 138–147 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  10. Freudenthal, H.: Einige Sätze über topologische Gruppen. Ann. of Math. (2),37, 46–56 (1936)

    Article  MathSciNet  Google Scholar 

  11. Freudenthal, H., de Vries, H.: Linear Lie Groups. New York-London: Academic Press, 1969

    Google Scholar 

  12. Grundhöfer, T., Salzmann, H.: Locally compact double loops and ternary fields. In: O. Chein, H.D. Pflugfelder, J.D.H. Smith (eds.), Quasigroups and Loops: Theory and Applications, Berlin: Heldermann 1990

    Google Scholar 

  13. Halder, H.R.: Dimension der Bahn lokal kompakter Gruppen. Arch. Math.22, 302–303 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hewitt, E., Ross, K.A.: Abstract Harmonic Analysis I, 2nd ed. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  15. Iwasawa, K.: On some types of topological groups. Ann. of Math.50, 507–558 (1949)

    Article  MathSciNet  Google Scholar 

  16. Löwen, R.: Topology and dimension of stable planes: On a conjecture of H. Freudenthal. J. Reine Angew. Math.343, 109–122 (1983)

    Google Scholar 

  17. Massey, W.S.: Singular Homology Theory: Berlin Heidelberg New York: Springer, 1980

    MATH  Google Scholar 

  18. Montgomery, D., Mostow, G.D.: Toroid transformation groups on euclidean space. Illinois J. Math.2, 459–481 (1958)

    MATH  MathSciNet  Google Scholar 

  19. Montgomery, D., Zippin, L.: Topological Transformation Groups. New York: Wiley 1955

    MATH  Google Scholar 

  20. Pears, A.R.: Dimension theory of general spaces. Cambridge University Press 1975

  21. Salzmann, H.: Topological planes. Adv. Math.2, 1–60 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  22. Salzmann, H.: Homogene kompakte projektive Ebenen. Pacific. J. Math.60, 217–234 (1975)

    MATH  MathSciNet  Google Scholar 

  23. Salzmann, H.: Automorphismengruppen achtdimensionaler Ternärkörper. Math. Z.166, 265–275 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  24. Salzmann, H.: Compact 8-dimensional projective planes with large collineation groups. Geom. Dedicata18, 139–161 (1979)

    MathSciNet  Google Scholar 

  25. Seidel, H.-P.: Locally homogeneous ANR-spaces. Arch. Math.44, 79–81 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  26. Smith, P.A.: New results and old problems in finite transformation groups. Bull. Am. Math. Soc.,66, 402–415 (1960)

    Article  Google Scholar 

  27. Spanier, E.H.: Algebraic Topology, New York: McGraw-Hill 1966

    MATH  Google Scholar 

  28. Tschetweruchin, N.: Eine Bemerkung zur den Nicht-Desarguesschen Liniensystemen. Jber. Deutsch. Math. Verein.36, 134–136 (1927), Fortschritte d. Math.53, 540 (1927)

    MATH  Google Scholar 

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Bödi, R. On the dimensions of automorphism groups of four-dimensional double loops. Math Z 215, 89–97 (1994). https://doi.org/10.1007/BF02571700

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