Let $F$ and $H$ be two free groups, where $F = \langle a,b\rangle$ and $H = \langle aa,bb,aba,baab, babab\rangle$. Let $N(H)$ be the normalizer of $H$ in $F$.

How can I compute $N(H)/H$?

In general, given a presentation of a group, is there a way to find its normalizer?

  • 2
    $\begingroup$ In general, questions about finitely presented groups are typically undecidable, and the answer is no. There is an algorithm for calculating the normalizer of a finitely generated subgroup of a free group.But the specific problem you ask is rather easy. As a hint, $|F:H|$ is finite. $\endgroup$ – Derek Holt Apr 29 '17 at 8:18

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