Semigroups of matrices of intermediate growth

Ferran Cedó; Jan Okniński

doi:10.1016/j.aim.2006.11.004

Semigroups of matrices of intermediate growth

Ferran Cedó, Jan Okniński

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	669-691
Journal	Advances in Mathematics
Volume	212
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2006.11.004
Publication status	Published - 10 Jul 2007

Keywords

Growth function
Linear semigroup
Nilpotent group
Semigroup
Subexponential growth

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abstract = "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. {\textcopyright} 2006 Elsevier Inc. All rights reserved.",

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AU - Cedó, Ferran

AU - Okniński, Jan

PY - 2007/7/10

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N2 - 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.

AB - 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.

KW - Growth function

KW - Linear semigroup

KW - Nilpotent group

KW - Semigroup

KW - Subexponential growth

U2 - 10.1016/j.aim.2006.11.004

DO - 10.1016/j.aim.2006.11.004

M3 - Article

VL - 212

SP - 669

EP - 691

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -