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

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arxiv 2410.17828 v1 pith:G7Y5VQ4H submitted 2024-10-23 math.GR math.CO

Marston Conder , Gabriel Verret , Darius Young This is my paper · ORCID
classification math.GRmath.CO
keywords densityordersgraphsnaturalapplicationsapplycasescharacterise
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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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  1. Edge-transitive cubic graphs: Cataloguing and Enumeration

    math.CO 2025-02 conditional novelty 6.0 of 10

    There are 4858 connected cubic edge-transitive graphs on up to 10000 vertices, and for each of the 22 amalgam types the number of graphs of order at most n grows like n^{Theta(log n)}.

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