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Ohkuma Structures

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Abstract

The construction and characterization by T. Ohkuma of a chain whose automorphism group acts uniquely transitively is extended in this article to analogues for circularly ordered sets and betweenness chains.

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References

  1. Conrad, P. F.: Right-ordered groups, Michigan Math. J. 6 (1959), 267–275.

    Google Scholar 

  2. Droste, M., Giraudet, M. and Macpherson, D.: Periodic ordered permutation groups and cyclic orderings, J. Combin. Theory B 63 (1995), 310–321.

    Google Scholar 

  3. Fuchs, L.: Partially Ordered Algebraic Systems, Addison-Wesley, Reading, Mass., 1963.

    Google Scholar 

  4. Glass, A. M. W.: Ordered Permutation Groups, London Math. Soc. Lecture Notes Ser. 55, Cambridge Univ. Press, 1981.

  5. Glass, A. M.W., Gurevich, Y., Holland, W. C. and Shelah, S.: Rigid homogeneous chains, Math. Proc. Cambridge Philos. Soc. 89 (1981), 7–17.

    Google Scholar 

  6. Holland, W. C.: Transitive lattice-ordered permutation groups, Math. Zeit. 87 (1965), 420–433.

    Google Scholar 

  7. Ohkuma, T.: Sur quelques ensembles ordonnés linéairement, Fund. Math. 43 (1955), 326–337.

    Google Scholar 

  8. Rieger, L. S.: On the ordered and cyclically ordered groups. I-III, V?stník Král. České Spol. Nauk, No. 6 (1946), 1-31; No. 1 (1947), 1-33; No. 1 (1948), 1-26 (Czech).

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Authors and Affiliations

  1. URA 753 Paris 7 CNRS/University of Le Mans, 32 Rue de la Réunion, 7502, Paris, France

    M. Giraudet

  2. Department of Mathematics, Bowling Green State University, Bowling Green, OH, 43403, U.S.A.

    W. C. Holland

Authors
  1. M. Giraudet
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  2. W. C. Holland
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Giraudet, M., Holland, W.C. Ohkuma Structures. Order 19, 223–237 (2002). https://doi.org/10.1023/A:1021249901409

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  • DOI: https://doi.org/10.1023/A:1021249901409

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