这篇论文把OpenAI找非sofic群的招数推广到了花环积，直接给出一类新的非sofic群，搞群论的朋友可以看看。
该论文基于OpenAI首次构造非sofic群的突破，分析其证明机制并给出新应用。设Γ与G均为具有性质(T)的群，且Γ在G中满足特定生成条件。若Γ非正规，则广义花环积(⊕_{G/Γ} Z/2Z)⋊G为非sofic群。这些假设在多项式环和Laurent多项式环上的初等群中成立，且两个群均为残有限和Kazhdan群。论文预印本编号为arXiv:2608.06222v1。
Nonsofic wreath products of residually finite groups
This work builds on the breakthrough of OpenAI in finding the first nonsofic group. We analyze the underlying proof mechanism and find further applications. Let $Γ<G$ be such that $\{g\in G:gΓg^{-1}\leqΓ\}$ generates $G$ as a group, and suppose that both $Γ$ and $G$ have property $(T)$. If $Γ$ is not normal, then the generalized wreath product $\bigl(\bigoplus_{G/Γ}\mathbb Z/2\mathbb Z\bigr)\rtimes G$ is nonsofic. These hypotheses hold for explicit pairs of elementary groups over polynomial and Laurent polynomial rings, in which both groups are residually finite and Kazhdan.