ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 5, 20, 51 Klin, Mikhail, Ben-Gurion University of the Negev, Israel On transitive permutation groups without semi-regular subgroups The following question is, to our knowledge, still open: find an example of a finite graph Γ with the vertex set V such that the automorphism group Aut(Γ) acts transitively on V and does not have a semi-regular subgroup. In our attempts to construct such an example we started from a few series of transitive permutation groups (H, V) about which it was known (W. M. Kantor) that they do not contain a semi-regular subgroup. We found 2-orbits of (H, V) and computed the 2-closure (H^{(2)}, V) (in the sense of Wielandt, see also reference). It turns out that the 2-closure does not have the desired property. This is joint work with G. Jones (Southampton). Reference: M. Ch. Klin, R. Pöschel, K. Rosenbaum, Angewandte Algebra. Einführung in gruppenteoretisch-kombinatorische Methoden. Vieweg, Braunschweig, 1988.