Abstract
A.M.W. Glass and S. H. McCleary have given the 2-transitive representation of the countable free l-group Fη (1 < η ⩽ ωo) (1<η⩽ω0). In this paper we shall give the highly ordered-transitive representation of countable free groups on the rational line Q, which generalizes their results. As applications, we obtain the highly ordered-transitive representation for the direct product of countable free groups,and the inverse limit of countable free groups must be an action on the set Q.
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References
Glass A. M. W., l-simple lattice-ordered groups, Proc. Edinburgh Math. Soc., 1974, 19:133–138
Glass A. M. W., Ordered Permutation Groups, London Math. Soc., Lecture Notes Series No. 55, The University Press, Cambridge, 1981
McCleary S.H, Free lattice-ordered groups represented as 0–2-transitive l-permutation groups, Trans. Amer. Math. Soc., 1985, 290:69–76
McCleary S. H, Free Lattice-Ordered Groups, Lattice-Ordered Groups, A. M. W. Glass and W. C. Holland,eds., Klwwer Academic Publishers, 1989
Anderson M. and Feil T., Lattice-Ordered Groups, D. Reidel Publishing Company, Dordrecht, Holland, 1988
Zhu Z., Huang J., The stability of l-permutation groups, J. Nanjing University, Math. Biquarterly, 1994, (1):6–9
Conrad P., The lateral completion of a lattice-ordered group, Proc. London Math. Soc., 1969, 19(3): 444–489
Rotman J., An Introduction to Homological Algebra, Academic Press, INC, 1979:39–48
Zhu Z., Chen Q., The Universal mapping problems of the l-group category, Chinese. Math., 1995, 23:17–21
Fuchs L., Partially ordered algebraic systems, Pergamon Press, New York, 1963
Glass A. M. W., Free products of lattice-ordered groups. Proc. Amer. Math. Soc., 1987, 101:11–16
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Lu, Bx., Zhu, Zt. Representations of free groups on rational line Q. J. of Shanghai Univ. 4, 101–105 (2000). https://doi.org/10.1007/s11741-000-0004-2
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DOI: https://doi.org/10.1007/s11741-000-0004-2