On the intersection of fixed subgroups of Fn×Fm
Abstract
We prove that, although it is undecidable if a subgroup fixed by an automorphism intersects nontrivially an arbitrary subgroup of [Formula: see text], there is an algorithm that, taking as input a monomorphism and an endomorphism of [Formula: see text], 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.
Fields of Study & Subjects
semigroups and automata theory
Geometric and Algebraic Topology
Finite Group Theory Research
Publication details
- Journal / source
- International Journal of Algebra and Computation
- Volume
- 36
- Issue
- 05
- Pages
- 487–499
- Publication date
- 6 February 2026
- Language
- EN