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Line-transitive collineation groups of finite projective spaces

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Abstract

A collineation group Γ ofPG(d, q), d ≧ 3, which is transitive on lines is shown to be 2-transitive on points unlessd=4,q=2 and |Γ|=31·5.

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References

  1. D. M. Bloom,The subgroups of PSL (3, q) for odd q, Trans. Amer. Math. Soc.127 (1967), 150–178.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Dembowski,Finite geometries, Springer, Berlin-Heidelberg-New York, 1968.

    MATH  Google Scholar 

  3. W. Feit and J. G. Thompson,Solvability of groups of odd order, Pacific J. Math.13 (1963), 771–1029.

    MathSciNet  Google Scholar 

  4. D. Gorenstein and J. H. Walter,The characterization of finite groups with dihedral Sylow 2-subgroups, I, II, III, J. Algebra3 (1965), 85–151, 218–270, 354–393.

    Article  MathSciNet  Google Scholar 

  5. D. G. Higman and J. E. McLaughlin,Geometric ABA-groups, Illinois J. Math.5 (1961), 382–397.

    MATH  MathSciNet  Google Scholar 

  6. W. M. Kantor,Automorphism groups of designs, Math. Z.109 (1969), 246–252.

    Article  MATH  MathSciNet  Google Scholar 

  7. W. M. Kantor,On 2-transitive collineation groups of finite projective spaces (to appear in Pacific J. Math.).

  8. D. Livingstone and A. Wagner,Transitivity of finite permutation groups on unordered sets, Math. Z.90 (1965), 393–403.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Lüneburg,Fahnenhomogene Quadrupelsysteme, Math. Z.89 (1965), 82–90.

    Article  MATH  MathSciNet  Google Scholar 

  10. H. M. Mitchell,Determination of the ordinary and modular ternary linear groups, Trans. Amer. Math. Soc.14 (1911), 207–242.

    Article  Google Scholar 

  11. D. Perin,On collineation groups of finite projective spaces, Math. Z.126, (1972), 135–142.

    Article  MATH  MathSciNet  Google Scholar 

  12. F. C. Piper,Elations of finite projective planes, Math. Z.82 (1963), 247–258.

    Article  MATH  MathSciNet  Google Scholar 

  13. I. Schur,Untersuchungen über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutionen, J. Reine Angew. Math.132 (1907), 85–137.

    Google Scholar 

  14. A. Wagner,On collineation groups of finite projective spaces I, Math. Z.76 (1961), 411–426.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Oregon, Eugene, Oregon, U.S.A.

    William M. Kantor

  2. University of Illinois, chicago, Illinois, U.S.A.

    William M. Kantor

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  1. William M. Kantor
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Research supported in part by NSF Grant GP 28420.

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Kantor, W.M. Line-transitive collineation groups of finite projective spaces. Israel J. Math. 14, 229–235 (1973). https://doi.org/10.1007/BF02764881

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  • DOI: https://doi.org/10.1007/BF02764881

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