-1
$\begingroup$

Let $F_\infty$ be the free group on infinitely many generators, and let $\phi: Z \rightarrow$ Aut($F_\infty$) be any group homomorphism. If we form the semi-direct product $F_\infty \rtimes_\phi Z$, could this group be isomorphic to $F_\infty$?

Thanks! Kevin

  • 2
    Also asked and answered [on MO](http://mathoverflow.net/questions/106472/could-f-infty-rtimes-z-be-isomorphic-to-f-infty). If you ask the same question on several sites, it would be nice to provide links between the various versions of the question to avoid duplication of effort.2012-09-06

1 Answers 1