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15.10 (2002)

Solved

(Yu. I. Merzlyakov). Is the group of all automorphisms of the free group $F_n$ that act trivially on $F_n/[F_n, F_n]$ linear for $n \geqslant 3$?

Contributor: V. G. Bardakov

Progress

No, it is not: for $n \geqslant 5$ (A. Pettet, Cohomology of some subgroups of the automorphism group of a free group, Ph.D. Thesis, 2006), and for $n \geqslant 3$ (V. G. Bardakov, R. Mikhailov, Commun. Algebra, 36, no. 4 (2008), 1489–1499).

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