Abstract
The following results are proved: Let E be a finite set, ¦E¦>4, and let G be a sharply 3-transitive permutation set on E. Then G contains no subset which is a sharply 2-transitive permutation set on E (Theorem 1). In the case when G is a sharply 3-transitive permutation group which is also planar, the finiteness condition on E can be dropped (Theorem 2).
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Dedicated to G. Zappa on his 70th birthday
Research done within the activity of GNSAGA of CNR, supported by the 40% grants of MPI.
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Quattrocchi, P. Over the non-existence of sharply 3-transitive permutation sets containing sharply 2-transitive permutation subsets. Geom Dedicata 23, 97–102 (1987). https://doi.org/10.1007/BF00147395
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DOI: https://doi.org/10.1007/BF00147395