{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T08:10:48Z","timestamp":1772439048386,"version":"3.50.1"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"05n06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2005,10]]},"abstract":"<jats:p> In this paper we discuss the problem: how large can the intermediate growth of nilpotent and relatively free semigroups be. We construct a sequence {S<jats:sub>n<\/jats:sub>} of finitely-generated semigroups such that the growth of the semigroup S<jats:sub>n+1<\/jats:sub> (n = 1,2,\u2026) is intermediate and larger than or equal to the growth of exp (m\/\u03c6<jats:sub>n<\/jats:sub>(m)), where \u03c6<jats:sub>n<\/jats:sub>(m) is the nth iteration of ln m. All semigroups S<jats:sub>n<\/jats:sub> are nilpotent in the sense of Malcev. We also find the sequence of relatively free semigroups with the same types of growth. <\/jats:p>","DOI":"10.1142\/s021819670500275x","type":"journal-article","created":{"date-parts":[[2006,1,4]],"date-time":"2006-01-04T19:48:36Z","timestamp":1136404116000},"page":"1189-1204","source":"Crossref","is-referenced-by-count":1,"title":["TYPES OF GROWTH AND IDENTITIES OF SEMIGROUPS"],"prefix":"10.1142","volume":"15","author":[{"given":"L. M.","family":"SHNEERSON","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Hunter College, The City University of New York, 695 Park Avenue, NY 10021, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"603","volume":"25","author":"Bass H.","journal-title":"Proc. London Math. Soc. 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