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On the intersection of fixed subgroups of Fn×Fm.

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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]
Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 194518550
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On the intersection of fixed subgroups of Fn×Fm.
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  Data: <searchLink fieldCode="AR" term="%22Carvalho%2C+André%22">Carvalho, André</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> andrecruzcarvalho@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Algebra+%26+Computation%22">International Journal of Algebra & Computation</searchLink>. Aug2026, Vol. 36 Issue 5, p487-499. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Endomorphisms%22">Endomorphisms</searchLink><br /><searchLink fieldCode="DE" term="%22Decidability+%28Mathematical+logic%29%22">Decidability (Mathematical logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Group+theory%22">Group theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematic+morphism%22">Mathematic morphism</searchLink><br /><searchLink fieldCode="DE" term="%22Free+groups%22">Free groups</searchLink><br /><searchLink fieldCode="DE" term="%22Automorphisms%22">Automorphisms</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0218196726500177
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 487
    Subjects:
      – SubjectFull: Endomorphisms
        Type: general
      – SubjectFull: Decidability (Mathematical logic)
        Type: general
      – SubjectFull: Group theory
        Type: general
      – SubjectFull: Mathematic morphism
        Type: general
      – SubjectFull: Free groups
        Type: general
      – SubjectFull: Automorphisms
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      – TitleFull: On the intersection of fixed subgroups of Fn×Fm.
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            – D: 01
              M: 08
              Text: Aug2026
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              Y: 2026
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            – TitleFull: International Journal of Algebra & Computation
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