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Mat. Zametki, 2002, Volume 71, Issue 1, Pages 122–129 (Mi mz333)  

On $\operatorname {c}$-3-Transitive Automorphism Groups of Cyclically Ordered Sets

V. M. Tararin

Institute of Applied Mathematical Research, Karelian Research Centre, RAS

Abstract: 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.

DOI: https://doi.org/10.4213/mzm333

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English version:
Mathematical Notes, 2002, 71:1, 110–117

Bibliographic databases:

UDC: 512.544.43
Received: 16.03.2001

Citation: V. M. Tararin, “On $\operatorname {c}$-3-Transitive Automorphism Groups of Cyclically Ordered Sets”, Mat. Zametki, 71:1 (2002), 122–129; Math. Notes, 71:1 (2002), 110–117

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