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<p>In this article we develop a notion of soficity for actions of countable groups on sets. We show two equivalent perspectives, several natural properties and examples. Notable examples include arbitrary actions of both amenable groups and free groups, and actions of sofic groups with locally finite stabilizers. As applications we prove soficity for generalized wreath products (and amalgamated free generalized wreath products) of sofic groups where the underlying group action is sofic. This generalizes the result of Hayes and Sale (Ann. Inst. Fourier 68:423-455, 2018), and proves soficity for many new families of groups.</p>

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Soficity for group actions on sets and applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月11日

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  • David Gao,
  • Srivatsav Kunnawalkam Elayavalli,
  • Gregory Patchell

摘要

In this article we develop a notion of soficity for actions of countable groups on sets. We show two equivalent perspectives, several natural properties and examples. Notable examples include arbitrary actions of both amenable groups and free groups, and actions of sofic groups with locally finite stabilizers. As applications we prove soficity for generalized wreath products (and amalgamated free generalized wreath products) of sofic groups where the underlying group action is sofic. This generalizes the result of Hayes and Sale (Ann. Inst. Fourier 68:423-455, 2018), and proves soficity for many new families of groups.