Gromov and Weiss's Question on Sofic Groups
Prior state unknown→disproved
answered no: non-sofic groups exist
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algebra / Geometric group theory
Gromov and Weiss's Question on Sofic Groups
Is every group sofic - does every group admit approximate finite permutation representations? A central open question of geometric group theory since Gromov introduced soficity: soficity implies Gottschalk's surjunctivity conjecture, Kaplansky's stable finiteness and more, and no non-sofic group was known. An explicit construction now establishes that non-sofic groups exist.
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Is every group sofic - does every group admit approximate finite permutation representations? A central open question of geometric group theory since Gromov introduced soficity: soficity implies Gottschalk's surjunctivity conjecture, Kaplansky's stable finiteness and more, and no non-sofic group was known. An explicit construction now establishes that non-sofic groups exist.
answered no: non-sofic groups exist
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