Bibliographic Details
| Title: |
On the intersection of fixed subgroups of Fn×Fm. |
| Authors: |
Carvalho, André1,2 (AUTHOR) andrecruzcarvalho@gmail.com |
| Source: |
International Journal of Algebra & Computation. Aug2026, Vol. 36 Issue 5, p487-499. 13p. |
| Subjects: |
Endomorphisms, Decidability (Mathematical logic), Group theory, Mathematic morphism, Free groups, Automorphisms |
| Abstract: |
We prove that, although it is undecidable if a subgroup fixed by an automorphism intersects nontrivially an arbitrary subgroup of F n × F m , there is an algorithm that, taking as input a monomorphism and an endomorphism of F n × 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
