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Relatively Free Semigroups of Intermediate Growth

✍ Scribed by L.M Shneerson

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
337 KB
Volume
235
Category
Article
ISSN
0021-8693

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✦ Synopsis

The problem of calculating the growth of a finitely generated f.g. semigroup satisfying the given system of identities is considered. Examples of relatively free semigroups having intermediate growth, new growth criteria, and constructions are given. The main ideas employed in the proofs are based on some new points of view on growth. Our method is also useful for constructing various examples of f.g. nilpotent and nil-semigroups having intermediate growth and arbitrarily small Gelfand᎐Kirillov superdimension. ᮊ 2001 Academic Press CONTENTS 1. Introduction.

2. Preliminaries.

  1. Growth criteria.

4. Constructions.

  1. On subexponential subsets of a free semigroup F . X 6. Growth and nilpotency for semigroups. 7. Upper bound for the growth of the semigroup F F .

3 8. Growth and Gelfand᎐Kirillo¨superdimension in semigroup ¨arieties.

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