# Given a presentation of a group, find its normalizer.

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?

• 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. – Derek Holt Apr 29 '17 at 8:18