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All groups are surjunctive

Authors :
Cannizzo, Jan
Publication Year :
2019

Abstract

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.<br />Comment: 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

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1912.00541
Document Type :
Working Paper