Abstract
A structure is said to be ‘Okhuma’ if its automorphism group acts on it uniquely transitively, or slightly generalizing this, if its automorphism group acts uniquely transitively on each orbit. In this latter case we can think of the orbits as ‘colours’. Okhuma chains and related structures have been studied by Okhuma and others. Here we generalize their results to coloured chains, and give some constructions resulting from this of Okhuma graphs and digraphs.
Similar content being viewed by others
References
Babai, L.: Finite digraphs with given regular automorphism groups, Period. Math. Hung. 11 (1980), 257–280.
Fuchs, L.: Partially Ordered Algebraic Systems, Pergamon Press, 1963.
Glass, A. M. W.: Ordered Permutation Groups, London Math. Soc. Lecture Notes 55, Cambridge University Press, 1981.
Glass, A. M. W., Gurevich, Yu., Holland, W. C. and Shelah, S.: Rigid homogeneous chains, Math. Proc. Cambridge Philos. Soc. 89 (1981), 7–17.
Giraudet, M. and Holland, C.: Okhuma structures, Order 19 (2002), 223–237.
Godsil, C. D.: GRRs for nonsolvable groups, in Algebraic Methods in Graph Theory, Vol. I, II (Szeged, 1978), Colloq. Math. Soc. Janos Bolyai 25, North-Holland, 1981, pp. 221–239.
Holland, W. C.: Transitive lattice ordered permutation groups, Math. Z. 87 (1965), 420–433.
Holland, W. C. and Rubin, M.: Semi-Okhuma chains, this issue of Order.
Okhuma, T.: Sur quelques ensembles ordonnés linéairement, Fund. Math. 43 (1955), 326–337.
Author information
Authors and Affiliations
Additional information
Mathematics Subject Classifications (2000)
06A05, 06F15.