Flag-transitivity and primitivity. (English) Zbl 0636.05008
An elementary argument is given to show that, for fixed \(\lambda\), there are only finitely many \(2\)-\((v,k,\lambda)\) designs having a flag-transitive and point-imprimitive automorphism group.
Reviewer: A. A. M. Cohen (Amsterdam)
MSC:
| 05B05 | Combinatorial aspects of block designs |
| 20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
References:
| [1] | Assmus, E. F.; Salwach, C. J., The (16, 6, 2) designs, Internat. J. Math. and Math. Sci., 2, 261-281 (1979) · Zbl 0424.05009 |
| [2] | Cameron, P.; Kantor, W., 2-transitive and antiflag collineation groups of finite projective spaces, J. Algebra, 60, 384-422 (1979) · Zbl 0417.20044 |
| [3] | Dembowski, P., Finite Geometries (1968), Springer: Springer Berlin · Zbl 0159.50001 |
| [4] | Wielandt, H., Finite Permutation Groups (1964), Academic Press: Academic Press New York · Zbl 0138.02501 |
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