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16.90 (2006)

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Is it true that the automorphism group $\text{Aut}\,F$ of an infinitely generated free group $F$ is
$\qquad$ a) the normal closure of a single element?
$\qquad$ b) the normal closure of some involution in $\text{Aut}\,F$?

Contributor: V. Tolstykh

Progress

For a free group $F_n$ of finite rank $n$, M. Bridson and K. Vogtmann have recently shown that $\text{Aut}\,F_n$ is the normal closure of some involution, which permutes some basis of $F_n$. It is also known that the automorphism groups of infinitely generated free nilpotent groups have such involutions.

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