Semigroups of matrices of intermediate growth

Autores: Ferran Cedó , Jan Okninski
Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 2, 2007, págs. 669-691
Idioma: inglés
DOI: 10.1016/j.aim.2006.11.004
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Resumen
- 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.