Linear growth for semigroups which are disjoint unions of finitely many copies of the free monogenic semigroup

2015/05/08 by Abughazalah, Nabilah, Etingof, Pavel
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1505.02149

Abstract

We show that every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) has linear growth. This implies that the the corresponding semigroup algebra is a PI algebra.

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• On disjoint unions of finitely many copies of the free monogenic semigroup
• Homogeneous finitely presented monoids of linear growth
• Families of linear semigroups with intermediate growth
• Growth and identities of monogenic free adequate monoids
• Subsemigroup, ideal and congruence growth of free semigroups