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arXiv · 2306.12533

On the intersection of fixed subgroups of $F_n\times F_m$

André Carvalho
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Abstract

We prove that, although it is undecidable if a subgroup fixed by an automorphism intersects nontrivially an arbitrary subgroup of $F_n\times F_m$, there is an algorithm that, taking as input a monomorphism and an endomorphism of $F_n\times F_m$, decides whether their fixed subgroups intersect nontrivially. The general case of this problem, where two arbitrary endomorphisms are given as input remains unknown. We show that, when two endomorphisms of a certain type are given as input, this problem is equivalent to the Post Correspondence Problem for free groups.

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André Carvalho. 2023-06-21. On the intersection of fixed subgroups of $F_n\times F_m$. https://arxiv.org/abs/2306.12533

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