Semigroups of matrices of intermediate growth

Ferran Cedó, Jan Okniński

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This 'growth alternative' conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)669-691
JournalAdvances in Mathematics
Issue number2
Publication statusPublished - 10 Jul 2007


  • Growth function
  • Linear semigroup
  • Nilpotent group
  • Semigroup
  • Subexponential growth


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