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arXiv · 2410.17828

Density of quotient orders in groups and applications to locally-transitive graphs

Marston Conder·Gabriel Verret·Darius Young
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Abstract

We prove that the set of orders of finite quotients of a finitely generated group has natural density 0, 1/2 or 1, and characterise when each of these cases occurs. We apply this to show that the sets of orders of various families of symmetric graphs have natural density 0.

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Marston Conder, Gabriel Verret, Darius Young. 2024-10-23. Density of quotient orders in groups and applications to locally-transitive graphs. https://arxiv.org/abs/2410.17828

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