Density of quotient orders in groups and applications to locally-transitive graphs
Group Theory
2024-10-24 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.2410.17828,
title = {Density of quotient orders in groups and applications to locally-transitive graphs},
author = {Marston Conder and Gabriel Verret and Darius Young},
journal= {arXiv preprint arXiv:2410.17828},
year = {2024}
}