The k-star Property for Permutation Groups

Rosemary Clough, Cheryl E. Praeger, Csaba Schneider

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Abstract

For an integer at least 2, a permutation group has the k-star property if, for every k-subset of points, contains an element that fixes it setwise but not pointwise. This property holds for all k-transitive, generously k-transitive, and almost generously k-transitive permutation groups. Study of the k-star property was motivated by recent work on the case = 3 by P. M. Neumann and the second author. The paper focuses on intransitive groups with the k-star property, studying properties of their transitive constituents, and relationships between the k-star and m-star properies for $\neq m$. Several open problems are posed.

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Published

2006-12-01

How to Cite

Team, S. (2006). The k-star Property for Permutation Groups: Rosemary Clough, Cheryl E. Praeger, Csaba Schneider. Thai Journal of Mathematics, 4(2), 251–256. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/46

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