, Volume 71, Issue 1-2, pp 110-117

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

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Abstract

An automorphism group $G$ of a cyclically ordered set $\left\langle {X,C} \right\rangle $ is said to be ${\text{c - 3}}$ -transitive if for any elements $x_i ,y_i \in {\text{X }},{\text{ }}i = 1,2,3$ , 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 ${\text{c - 3}}$ -transitive, then it is simple. A description of ${\text{c - 3}}$ -transitive automorphism groups with Abelian two-point stabilizer is given.