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September 18, 2025Proceedings of the Edinburgh Mathematical Society

The conjugacy ratio of abelian-by-cyclic groups

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DGDavid Guo

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Overview

This analysis reveals the conjugacy ratio of groups like BS(1,k) with a one-sided Følner sequence, indicating complexities in group structure.

Key Points

  • The conjugacy ratio of G is 0 unless it is virtually abelian, confirming a conjecture by prior researchers.
  • The Baumslag–Solitar group shows a non-zero conjugacy ratio with a one-sided Følner sequence, despite not being virtually abelian.
  • Two-sided Følner sequences yield a positive conjugacy ratio only for virtually abelian groups, as shown by Tointon.
  • Spherical conjugacy ratios mirror the findings for the general conjugacy ratio within this context.

Cite This Study

David Guo (2025) studied this question.

synapsesocial.com/papers/68d462c131b076d99fa61d57https://doi.org/10.1017/s0013091525100977
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