Geodesic
On $\operatorname {c}$-3-Transitive Automorphism Groups of Cyclically Ordered Sets
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 122-129

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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},
     publisher = {mathdoc},
     volume = {71},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a10/}
}
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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/