On Semigroups of Intermediate Growth

Abstract

We prove that intermediate growth of finitely generated (f.g.) semigroups can be arbitrarily large. Namely, for every monotone non-decreasing mapping f :  N  →  R ⁺ such that f(m) = o(c ^m ) for any c > 1, we construct a 2-generated semigroup whose growth is larger than the growth of f, but smaller than exponential.

Key Words:

• Rees-factor semigroup
• Infinite word
• Growth function

Acknowledgments

This work has been partially supported by the US National Security Agency Mathematical Sciences Program (Grant#MDA904-03-1-0084) and the PSC-CUNY Research Award Program.

Notes

^#Communicated by E. Zelmanov.