Forum Problem Lists Definitions FAQ

16.7 (2006)

Open

Is it true that the membership problem is undecidable for any semidirect product $F_n \rtimes F_n$ of non-abelian free groups $F_n$?

An affirmative answer would imply an answer to 6.24. Recall that the membership problem is decidable for $F_n$ (M. Hall, 1949) and undecidable for $F_n \times F_n$ (K. A. Mikhailova, 1958).

Contributor: V. G. Bardakov

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