Symmetrische Permutationsmengen |
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Authors: | Helmut Karzel |
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Institution: | (1) Institut für Mathematik der TU, D-8 München 2, Germany |
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Abstract: | A permutation set (M, I) consisting of a setM and a set of permutations ofM, is calledsymmetric, if for any two permutations, the existence of anx M with (x) (x) and
–1
(x) =
–1
(x) implies
–1
=
–1
, andsharply 3-transitive, if for any two triples (x
1,x
2,x
3), (y
1,y
2,y
3) M
3 with|{x
1,x
2,x
3
}| = |{y
1,y
2,y
3
}| = 3 there is exactly one permutation with(x
1) =y
1,(x
2) =y
2,(x
3) =y
3. The following theorem will be proved.THEOREM.Let (M, ) be a sharply 3-transitive symmetric permutation set with |M|3, such that contains the identity. Then is a group and there is a commutative field K such that and the projective linear group PGL(2, K) are isomorphic. |
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Keywords: | Primary 20B10 20G05 |
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