On the inverse semigroups of intermediate growth

L. M. Shneyerson

*City University of New York, USA*

In [1] we presented a method for constructing different types of
examples of finitely generated (f.g.) semigroups having intermediate
growth.

Recently we found a family of examples of f.g. semigroups whose growth is
intermediate but very close to exponential. Here we discuss the following

**Problem.** * How small or large can the intermediate growth of
f.g. inverse semigroups be?*

In particular we give the first examples of f.g. inverse semigroups of
intermediate growth having minimal (equal to 0) and maximal (equal to 1)
Gelfand-Kirillov superdimension.

A part of the talk is a joint work with A. Peluso.

### References

[1] L. M. Shneerson, Relatively free semigroups of intermediate
growth, J. Algebra **235** (2001), 484-546.

Sponsored in part by the FCT approved
projects POCTI 32817/99 and POCTI/MAT/37670/2001 in participation with
the European Community Fund FEDER and by FCT through *Centro de Matemática
da Universidade do Porto.* Also sponsored in part by FCT, the
*Faculdade de Ciências da Universidade do Porto, Programa Operacional Ciência, Tecnologia, Inovação do Quadro Comunitário de Apoio III*, and by *Caixa Geral de Depósitos*.

File translated from T_{E}X by T_{T}H, version 1.92.

On 29 Apr 2002, 18:40.