ON THE ORDER OF ARC-STABILIZERS IN ARC-TRANSITIVE GRAPHS

摘要

An exhaustive computer search through a library of transitive group actions of small degree reveals that, apart from A5 acting on the vertices of the dodecahedron, all psub- regular actions of degree at most 26 appear in at least one of the six infinite families listed above. Some of theses actions are primitive and hence part of our work can be viewed as an effort towards the Weiss conjecture. On the other hand, the imprimitive actions also need to be considered in view of the more general Problem 1.3. From the perspective of this problem, most of the past efforts have been concentrating on the locally primitive graphs, thus working in the setting of the Weiss conjecture. We hope that our results will spur further investigation of arc-stabilizers in locally imprimitive graphs, and perhaps shed new light on the problem of bounding the order of arcstabilizers in arc-transitive graphs in general.