{"id":"palomar/PALOMAR-2026-09-14-000002","url":"https://github.com/SauersML/group-approximation/tree/232c77f169ec66b27fd480d5c19474f519d359b7","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-14-000002-v1.json","repo":"https://github.com/SauersML/group-approximation","tags":["math.GR","math.DS","msc:20F69","msc:37B15","msc:20E06","group-theory","sofic-groups","surjunctivity"],"score":0,"title":"A Surjunctive Group That Is Not Sofic","trust":"high","domain":"math.GR","source":"palomar","authors":["Sauers"],"reviews":0,"subject":"math.GR","summary":"We formalize the existence of a finitely generated surjunctive group that is not sofic. This answers negatively the converse to the Gromov-Weiss surjunctivity theorem, recorded as open problem OP-11 by Ceccherini-Silberstein and Coornaert and as Problem 1.1 by Bowen and Chapman. The witness is the symmetric double G *_Gamma G, where Gamma = EL_3(F_2[x_1,x_2,x_3]) and G = EL_3(F_2[x_1^+-1,x_2^+-1,x_3^+-1]) semidirect EL_3(Z), with the action given by monomial substitution. Kun and Thom constructed this pair and proved the double nonsofic. The new ingredient here is a surjunctivity theorem for…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-14","reactions":{},"formalized":true}