The Ribes-Zalesskiĭ product theorem via foldings and extensions

2025/09/08 by Zhaoshen Zhai, Zhai, Zhaoshen
Computer Science · #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2509.06877

Abstract

We present an exposition of the Auinger-Steinberg proof of the Ribes-Zalesskiĭ product theorem for pro-V topologies, where V is a pseudovariety of groups closed under extensions with abelian kernel. This proof is self-contained and is accessible to those acquainted with coverings of graphs, and as such, it provides an easy entry point to various other deep theorems for which the product theorem is formally equivalent to.

Citations

• Finite approximation of free groups II: the Theorems of Ash, Herwig-Lascar and Ribes-Zalesskii -- revisited and strengthened
• The Hrushovski property for hypertournaments and profinite topologies
• Formations of finite groups with the M. Hall property
• Generic representations of countable groups
• The geometry of profinite graphs revisited
• A survey on structural Ramsey theory and topological dynamics with the Kechris-Pestov-Todorcevic correspondence in mind
• Finitely approximable groups and actions Part I: The Ribes--Zalesski\uı property
• Automorphism groups of saturated structures; a review

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