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arXiv 1912.00541math.DSmath.GR
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所有的群都是超连词

All groups are surjunctive

Jan Cannizzo

备注：
As several people have pointed out to me, the last sentence of Lemma 5.3 is not justified. This likely counts as a fatal flaw that invalidates the main theorem (Theorem 5.4). I would like to thank those who took the time to read the preprint and send me their feedback. I hereby retract the claimed result
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摘要：

本文证明了对有限生成群$G$和任意的$k\geq1$，$G$的$k$ -着色空间不允许严格的自嵌入.这解决了Gottschalk的替代性猜想，因此，Kaplansky的直接有限性猜想。

英文摘要：

We prove that for any finitely generated group $G$ and any $k\geq1$, the space of $k$-colorings of $G$ does not admit a strict self-embedding. This settles the Gottschalk surjunctivity conjecture and, consequently, Kaplansky's direct finiteness conjecture.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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