A Surjunctive Group That Is Not Sofic
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…
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