TYPES OF GROWTH AND IDENTITIES OF SEMIGROUPS
L. M. Shneerson · International Journal of Algebra and Computation · 2005
In this paper we discuss the problem: how large can the intermediate growth of nilpotent and relatively free semigroups be. We construct a sequence {Sn} of finitely-generated semigroups such that the growth of the semigroup Sn+1 (n = 1,2,…) is intermediate and larger than or equal to the growth of exp (m/φn(m)), where φn(m) is the nth iteration of ln m. All semigroups Sn are nilpotent in the sense of Malcev. We also find the sequence of relatively free semigroups with the same types of growth.