{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:14:06Z","timestamp":1758280446035},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p>For any positive integer n &gt; 1 we construct an example of inverse semigroup with n generators and n - 1 defining relations which has cubic growth and at least n generators in any presentation. This semigroup has the same set of identities as the free monogenic inverse semigroup. In particular, we give the first example of a one relation nonmonogenic inverse semigroup having polynomial growth. We also prove that for any positive integer n there exists an inverse semigroup \u03d2<jats:sub>n<\/jats:sub>of deficiency 1 and rank n + 1 such that \u03d2<jats:sub>n<\/jats:sub>has exponential growth and it does not contain nonmonogenic free inverse subsemigroups. Furthermore, \u03d2<jats:sub>n<\/jats:sub>satisfies the identity [[x, y], [z, t]]<jats:sup>2<\/jats:sup>= [[x, y], [z, t]] of quasi-solvability and it contains a free subsemigroup of rank 2.<\/jats:p>","DOI":"10.1142\/s0218196715400093","type":"journal-article","created":{"date-parts":[[2015,1,9]],"date-time":"2015-01-09T08:33:15Z","timestamp":1420792395000},"page":"233-258","source":"Crossref","is-referenced-by-count":3,"title":["On growth, identities and free subsemigroups for inverse semigroups of deficiency one"],"prefix":"10.1142","volume":"25","author":[{"given":"L. 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