5.49 (1976)
SolvedLet $A_{m,n}$ be the group of all automorphisms of the free soluble group of derived length $n$ and rank $m$. Is it true that
$\qquad$ a) $A_{m,n}$ is finitely generated for any $m$ and $n$?
$\qquad$ b) every automorphism in $A_{m,n}$ is induced by some automorphism in $A_{m,n+1}$?
Progress
a) No: $A_{3,2}$ is not finitely generated, although $A_{m,2}$ is whenever $m \neq 3$ (S. Bachmuth, H. Y. Mochizuki, Trans. Amer. Math. Soc., 270 (1982), 693–700, 292 (1985), 81–101).
b) No (V. Shpilrain, Int. J. Algebra and Comput., 1, no. 2 (1991), 177–184).
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