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A Tits alternative for endomorphisms of the projective line.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος: A Tits alternative for endomorphisms of the projective line.
Συγγραφείς: Bell, Jason P., Keping Huang, Wayne Peng, Tucker, Thomas J.
Πηγή: Journal of the European Mathematical Society (EMS Publishing); 2024, Vol. 26 Issue 12, p4903-4922, 20p
Θεματικοί όροι: Endomorphisms, Semigroup algebras, Nonabelian groups, Semigroups (Algebra), Program generators (Computer programs)
Περίληψη: We prove an analog of the Tits alternative for endomorphisms of P1. In particular, we show that if S is a finitely generated semigroup of endomorphisms of P1 over C, then either S has polynomially bounded growth or S contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field of any characteristic and Prep.f / 6D Prep.g/, then for all sufficiently large j, the semigroup hf j; gj i is a free semigroup on two generators. [ABSTRACT FROM AUTHOR]
Copyright of Journal of the European Mathematical Society (EMS Publishing) is the property of European Mathematical Society - EMS - Publishing House GmbH 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.)
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IllustrationInfo
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  Data: A Tits alternative for endomorphisms of the projective line.
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  Data: <searchLink fieldCode="AR" term="%22Bell%2C+Jason+P%2E%22">Bell, Jason P.</searchLink><br /><searchLink fieldCode="AR" term="%22Keping+Huang%22">Keping Huang</searchLink><br /><searchLink fieldCode="AR" term="%22Wayne+Peng%22">Wayne Peng</searchLink><br /><searchLink fieldCode="AR" term="%22Tucker%2C+Thomas+J%2E%22">Tucker, Thomas J.</searchLink>
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  Data: Journal of the European Mathematical Society (EMS Publishing); 2024, Vol. 26 Issue 12, p4903-4922, 20p
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  Data: <searchLink fieldCode="DE" term="%22Endomorphisms%22">Endomorphisms</searchLink><br /><searchLink fieldCode="DE" term="%22Semigroup+algebras%22">Semigroup algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Nonabelian+groups%22">Nonabelian groups</searchLink><br /><searchLink fieldCode="DE" term="%22Semigroups+%28Algebra%29%22">Semigroups (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Program+generators+%28Computer+programs%29%22">Program generators (Computer programs)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We prove an analog of the Tits alternative for endomorphisms of P1. In particular, we show that if S is a finitely generated semigroup of endomorphisms of P1 over C, then either S has polynomially bounded growth or S contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field of any characteristic and Prep.f / 6D Prep.g/, then for all sufficiently large j, the semigroup hf j; gj i is a free semigroup on two generators. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of the European Mathematical Society (EMS Publishing) is the property of European Mathematical Society - EMS - Publishing House GmbH 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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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.4171/JEMS/1376
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 20
        StartPage: 4903
    Subjects:
      – SubjectFull: Endomorphisms
        Type: general
      – SubjectFull: Semigroup algebras
        Type: general
      – SubjectFull: Nonabelian groups
        Type: general
      – SubjectFull: Semigroups (Algebra)
        Type: general
      – SubjectFull: Program generators (Computer programs)
        Type: general
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      – TitleFull: A Tits alternative for endomorphisms of the projective line.
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            NameFull: Keping Huang
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            NameFull: Wayne Peng
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            – D: 01
              M: 12
              Text: 2024
              Type: published
              Y: 2024
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              Value: 26
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              Value: 12
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