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Keywords:
transitive $l$-permutation group; stabilizer subgroup; primitive component; normal-valued $l$-group.
transitive $l$-permutation group; stabilizer subgroup; primitive component; normal-valued $l$-group.
Summary:
We give some necessary and sufficient conditions for transitive $l$-permutation groups to be $2$-transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive $l$-permutation groups to be normal-valued.
References:
[1] W. C. Holland: Transitive lattice-ordered permutation groups. Math. Zeit. 87 (1965), 420–433; MR31 (1966), # 2310. DOI 10.1007/BF01111722 | MR 0178052 | Zbl 0147.01204
[2] A. M. W. Glass: Ordered Permutation Groups. Cambridge University Press, 1981, pp. 76–116. MR 0645351 | Zbl 0473.06010
[3] Z. T. Zhu and J. M. Huang: Stability of $l$-permutation groups. J. of Nanjing Uni. Math. Biquarterly 11, No. 1 (1994), 18–21. MR 1293882
[4] M. Anderson and T. Feil: Lattice-Ordered Groups. D. Reidel Publishing Company, Dordrecht, Holland, 1988, pp. 29–31. MR 0937703
[5] Z. T. Zhu and J. M. Huang: Congruent pairs on a set. Chinese Quarterly Journal of Math. 9, No. 3 (1994), 37–41.
[6] S. H. McClearly: The structure of intransitive ordered permutation groups. Algebra Universalis 6 (1976), 229–255. DOI 10.1007/BF02485831 | MR 0424638
[7] A. M. W. Glass: Elementary types of automorphisms of linearly ordered sets—a survey. Algebra, Carbondale 1980, R.K. Amayo (ed.), Springer, Lecture Notes No. 848, pp. 218–229. MR 0613188 | Zbl 0466.06016
[8] S. H. McClearly: The structure of ordered permutation groups applied to lattice-ordered groups. Notices Amer. Math. Soc., 21 (1974), February, # 712–714, PA336.
[9] Z.T. Zhu and Q. Chen: The universal mapping problems of the $l$-group category. Chinese Journal of Math. 23, No. 2 (1995), 131–140. MR 1340760
[10] A. M. W. Glass and W. C. Holland (Eds): Lattice-Ordered Groups. Kluwer Academic Publishers, 1989, pp. 23–40. MR 1036072
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