Arc-transitive graphs of valency twice a prime admit a semiregular\n automorphism

2018/12/31 by Michael Giudici, Giudici, Michael, Gabriel Verret +1 · 1 citation
Mathematics · #Finite Group Theory Research #Advanced Topics in Algebra #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1901.00084

Abstract

We prove that every finite arc-transitive graph of valency twice a prime\nadmits a nontrivial semiregular automorphism, that is, a non-identity\nautomorphism whose cycles all have the same length. This is a special case of\nthe Polycirculant Conjecture, which states that all finite vertex-transitive\ndigraphs admit such automorphisms.\n

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