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Semigroups of matrices of intermediate growth
Cedó i Giné, Ferran; Okniski, Jan
Centre de Recerca Matemàtica
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.
2006-08
512 - Àlgebra
512 - Àlgebra
Semigrups
Matrius (Matemàtica)
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