, 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.