Mathematical Notes

, Volume 71, Issue 1, pp 110–117

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

Authors

  • V. M. Tararin
    • Institute of Applied Mathematical Analysis Karelian Research CenterRussian Academy of Sciences
Article

DOI: 10.1023/A:1013934509265

Cite this article as:
Tararin, V.M. Mathematical Notes (2002) 71: 110. doi:10.1023/A:1013934509265
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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.

cyclic orderautomorphism groupsimple grouptransitivitystabilizer
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© Plenum Publishing Corporation 2002