Splitting groups with cubic Cayley graphs of connectivity two

Abstract

A group $G$ splits over a subgroup $C$ if $G$ is either a free product with amalgamation $A\underset{C}{\ast }B$ or an HNN-extension $G=A\underset{C}{\ast }(t)$. We invoke Bass-Serre theory and classify all infinite groups which admit cubic Cayley graphs of connectivity two in terms of splittings over a subgroup.

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References in corpus (3)

• Almost square permutations are typically square
• Permutations with few inversions are locally uniform
• Scaling limits of permutation classes with a finite specification: a dichotomy

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