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2.61 (1966)

Solved

Let $\Gamma$ be a Noetherian group of automorphisms of a vector space $G$ such that every element of $\Gamma$ is unipotent. Is $\Gamma$ necessarily a stable group of automorphisms?

Contributor: B. I. Plotkin

Progress

Not if the field has non-zero characteristic (A. Yu. Olshanskii, The geometry of defining relations in groups, Kluwer, Dordrecht, 1991). This is true for fields of characteristic zero if the indices of unipotence are uniformly bounded (B. I. Plotkin, S. M. Vovsi, Varieties of group representations, Zinatne, Riga, 1983 (Russian)).

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