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. © Cambridge Philosophical Society 2014..

Spiga, P. (2014). Semiregular elements in cubic vertex-transitive graphs and the restricted Burnside problem. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 157(1), 45-61 [10.1017/S0305004114000188].

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

SPIGA, PABLO
2014

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. © Cambridge Philosophical Society 2014..
Articolo in rivista - Articolo scientifico
Mathematics (all)
English
2014
157
1
45
61
none
Spiga, P. (2014). Semiregular elements in cubic vertex-transitive graphs and the restricted Burnside problem. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 157(1), 45-61 [10.1017/S0305004114000188].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/99788
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