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Affine Rank 3 Groups on Symmetric Designs

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Abstract

In this note we determine the symmetric designs which admit a primitive rank 3 group with a solvable normal subgroup. This completes the investigations of Dempwolff [4].

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References

  1. G. Bell, Cohomology of degree 1 and 2 of the Suzuki groups, Pac. J. Math., Vol. 75 (1978) pp. 319-329.

    Google Scholar 

  2. J. Conway, R. Curtis, S. Norton, R. Parker and R. Wilson, An ATLAS of finite groups, Oxford University Press (1985).

  3. U. Dempwolff, On extensions of elementary abelian 2-groups by ∑n, Glasnick Matematicki, Vol. 14 (1979) pp. 35-40.

    Google Scholar 

  4. U. Dempwolff, Primitive rank 3 groups on symmetric designs, Designs, Codes, and Cryptography, Vol. 22 (2001) pp. 191-207.

    Google Scholar 

  5. J. F. Dillon, Elementary Hadamard difference sets, In Proc. 6th S.E. Conf. Combinatorics, Graph Theory and Computing, Utilitas Math., Boca Raton (1975) pp. 237-249.

    Google Scholar 

  6. D. Foulser, Solvable primitive permutation groups of low rank, Trans. Amer. Math Soc., Vol. 143 (1969) pp. 1-54.

    Google Scholar 

  7. D. Foulser and M. Kallaher, Solvable flag-transitive rank 3 collineation groups, Geom. Ded., Vol. 7 (1978) pp. 111-136.

    Google Scholar 

  8. D. Higman, Finite permutation groups of rank three, Math. Z., Vol. 86 (1964) pp. 145-156.

    Google Scholar 

  9. B. Huppert, Endliche Gruppen I, Springer (1967).

  10. C. Jansen, K. Lux, R. Parker and R. Wilson, An Atlas of Brauer Characters, Oxford University Press (1995).

  11. W. Jones and B. Parshall, On the 1-cohomology of finite groups of Lie-type, In W. Scott and F. Gross ed., Proc. Conf. Finite Groups 1975, Academic Press (1976) pp. 313-327.

  12. W. Kantor, Symplectic groups, symmetric designs and line ovals, Jour. Alg., Vol. 33 (1975) pp. 43-58.

    Google Scholar 

  13. W. Kantor, Classification of 2-transitive symmetric designs, Graphs and Combin., Vol. 1 (1985) pp. 165-166.

    Google Scholar 

  14. W. Kantor and R. Liebler, The rank 3 permutation representations of the finite classical groups, Trans. Amer. Math. Soc., Vol. 271 (1982) pp. 1-71.

    Google Scholar 

  15. M. Liebeck, The affine permutation groups of rank 3, Proc. Lond. Math. Soc. III Ser., Vol. 54 (1987) pp. 477-516.

    Google Scholar 

  16. H. Mann, Difference sets in elementary abelian groups, Ill. Jour. Math., Vol. 9 (1965) pp. 212-219.

    Google Scholar 

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  1. FB Mathematik, Universitaet, 67653, Kaiserslautern, Germany

    U. Dempwolff

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  1. U. Dempwolff
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Dempwolff, U. Affine Rank 3 Groups on Symmetric Designs. Designs, Codes and Cryptography 31, 159–168 (2004). https://doi.org/10.1023/B:DESI.0000012444.37411.1c

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  • DOI: https://doi.org/10.1023/B:DESI.0000012444.37411.1c

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