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Semiregular elements in cubic vertex-transitive graphs and the restricted Burnside problem

Published online by Cambridge University Press:  15 April 2014

PABLO SPIGA
PABLO SPIGA*
Affiliation:
Dipartimento di Matematica Pura e Applicata, University of Milano-Bicocca, Via Cozzi 55, 20126 Milano, Italy. e-mail: [email protected]
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Abstract

In this paper, we prove that the maximal order of a semiregular element in the automorphism group of a cubic vertex-transitive graph Γ does not tend to infinity as the number of vertices of Γ tends to infinity. This gives a solution (in the negative) to a conjecture of Peter Cameron, John Sheehan and the author [4, conjecture 2].

However, with an application of the positive solution of the restricted Burnside problem, we show that this conjecture holds true when Γ is either a Cayley graph or an arc-transitive graph.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 1 , July 2014 , pp. 45 - 61
Copyright
Copyright © Cambridge Philosophical Society 2014 

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