The Tits Alternative for two-dimensional Artin groups and Wise's Power Alternative

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Abstract

We show that two-dimensional Artin groups satisfy a strengthening of the Tits alternative: their subgroups either contain a non-abelian free group or are virtually free abelian of rank at most 2.

When in addition the associated Coxeter group is hyperbolic, we answer in the affirmative a question of Wise on the subgroups generated by large powers of two elements: given any two elements a, b of a two-dimensional Artin group of hyperbolic type, there exists an integer n ≥ 1 such that an and bn either commute or generate a non-abelian free subgroup.
Original languageEnglish
JournalJournal of Algebra
Early online date28 Aug 2023
DOIs
Publication statusE-pub ahead of print - 28 Aug 2023

Keywords

  • Artin groups
  • Tits alternative

ASJC Scopus subject areas

  • Algebra and Number Theory

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