Automorphisms of free bicommutative algebras over an arbitrary field are studied. Wild automorphisms are constructed in two-generated and three-generated free bicommutative algebras. Moreover, for any n≥2, a wild automorphism is constructed in the n-generated free associative bicommutative algebra which is not stably tame and can not be lifted to an automorphism of the n-generated free bicommutative algebra.
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Shestakov et al. (2020) studied this question.