| Title:
|
The structure of transitive ordered permutation groups (English) |
| Author:
|
Zhu, Zuo-Tong, |
| Author:
|
Zhenyu, Huang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
811-815 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
transitive $l$-permutation group |
| Keyword:
|
stabilizer subgroup |
| Keyword:
|
primitive component |
| Keyword:
|
normal-valued $l$-group. |
| MSC:
|
06C15 |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1007.06012 |
| idMR:
|
MR1746705 |
| . |
| Date available:
|
2009-09-24T10:27:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127529 |
| . |
| Reference:
|
[1] W. C. Holland: Transitive lattice-ordered permutation groups.Math. Zeit. 87 (1965), 420–433; MR31 (1966), # 2310. Zbl 0147.01204, MR 0178052, 10.1007/BF01111722 |
| Reference:
|
[2] A. M. W. Glass: Ordered Permutation Groups.Cambridge University Press, 1981, pp. 76–116. Zbl 0473.06010, MR 0645351 |
| Reference:
|
[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 |
| Reference:
|
[4] M. Anderson and T. Feil: Lattice-Ordered Groups.D. Reidel Publishing Company, Dordrecht, Holland, 1988, pp. 29–31. MR 0937703 |
| Reference:
|
[5] Z. T. Zhu and J. M. Huang: Congruent pairs on a set.Chinese Quarterly Journal of Math. 9, No. 3 (1994), 37–41. |
| Reference:
|
[6] S. H. McClearly: The structure of intransitive ordered permutation groups.Algebra Universalis 6 (1976), 229–255. MR 0424638, 10.1007/BF02485831 |
| Reference:
|
[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. Zbl 0466.06016, MR 0613188 |
| Reference:
|
[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. |
| Reference:
|
[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 |
| Reference:
|
[10] A. M. W. Glass and W. C. Holland (Eds): Lattice-Ordered Groups.Kluwer Academic Publishers, 1989, pp. 23–40. MR 1036072 |
| . |
