Gottschalk's surjunctivity conjecture

The group $G$ and elements $a,b\in K[G]$ of the characteristic-two direct-finiteness counterexample ($K$ finite, $G$ finitely presented with odd torsion) define a cellular automaton on $K^G$ that is injective but not surjective, so $G$ is not surjunctive. The odd-characteristic companion (September 26) gives the same conclusion over a field of order $p^4$ for a finitely generated group with torsion. The automata are linear; no torsion-free non-surjunctive group is claimed in these papers (the torsion-free companion does not discuss automata).

The group $G$ and elements $a,b\in K[G]$ of the characteristic-two direct-finiteness counterexample ($K$ finite, $G$ finitely presented with odd torsion) define a cellular automaton on $K^G$ that is injective but not surjective, so $G$ is not surjunctive. The odd-characteristic companion (September 26) gives the same conclusion over a field of order $p^4$ for a finitely generated group with torsion. The automata are linear; no torsion-free non-surjunctive group is claimed in these papers (the torsion-free companion does not discuss automata).