Geodesic
On $\operatorname {c}$-3-Transitive Automorphism Groups of Cyclically Ordered Sets
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 122-129 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An automorphism group $G$ of a cyclically ordered set $\langle X,C\rangle $ is said to be $\operatorname {c}$-3-transitive if for any elements $x_i,y_i\in X$ ($i=1,2,3$), such that $C(x_1,x_2,x_3)$ and $C(y_1,y_2,y_3)$ there exists an element $g\in G$ satisfying $g(x_i)=y_i$, $i=1,2,3$. We prove that if an automorphism group of a cyclically ordered set is $\operatorname {c}$-3-transitive, then it is simple. A description of $\operatorname {c}$-3-transitive automorphism groups with Abelian two-point stabilizer is given. 
@article{MZM_2002_71_1_a10,
     author = {V. M. Tararin},
     title = {On $\operatorname {c}${-3-Transitive} {Automorphism} {Groups} of {Cyclically} {Ordered} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {122--129},
     year = {2002},
     volume = {71},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a10/}
}
TY  - JOUR
AU  - V. M. Tararin
TI  - On $\operatorname {c}$-3-Transitive Automorphism Groups of Cyclically Ordered Sets
JO  - Matematičeskie zametki
PY  - 2002
SP  - 122
EP  - 129
VL  - 71
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a10/
LA  - ru
ID  - MZM_2002_71_1_a10
ER  - 
%0 Journal Article
%A V. M. Tararin
%T On $\operatorname {c}$-3-Transitive Automorphism Groups of Cyclically Ordered Sets
%J Matematičeskie zametki
%D 2002
%P 122-129
%V 71
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a10/
%G ru
%F MZM_2002_71_1_a10
V. M. Tararin. On $\operatorname {c}$-3-Transitive Automorphism Groups of Cyclically Ordered Sets. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 122-129. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a10/

[1] Fuks L., Chastichno uporyadochennye algebraicheskie sistemy, Mir, M., 1965

[2] Kopytov V. M., Reshetochno uporyadochennye gruppy, Nauka, M., 1984 | Zbl

[3] Higman G., “The units of groups rings”, Proc. London Math. Soc., 46:2 (1940), 231–248 | DOI | MR | Zbl

[4] Tararin V. M., “$\operatorname{O}$-$2$-tranzitivnye gruppy avtomorfizmov s abelevym stabilizatorom tochki”, Matem. zametki, 65:2 (1999), 289–293 | MR | Zbl

[5] Fuks L., Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977

[6] Kokorin A. I., Kopytov V. M., Lineino uporyadochennye gruppy, Nauka, M., 1972 | Zbl

[7] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, 3-e izd., Nauka, M., 1982 | Zbl