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Finite nilpotent semigroups constitute a pseudovariety, MN, which has finite rank. The semigroup identities that define nilpotent semigroups lead us to define strongly Mal\u2019cev nilpotent semigroups. Finite strongly Mal\u2019cev nilpotent semigroups constitute a non-finite rank pseudovariety, SMN. The pseudovariety SMN is strictly contained in the pseudovariety MN, but all finite nilpotent groups are in SMN. We show that the pseudovariety MN is the intersection of the pseudovariety BGnil with a pseudovariety defined by a \u03ba-identity. We further compare the pseudovarieties MN and SMN with the Mal\u2019cev product \ud835\udda9\u24dc\ud835\udda6nill.<\/jats:p>","DOI":"10.1093\/qmath\/hay059","type":"journal-article","created":{"date-parts":[[2018,10,16]],"date-time":"2018-10-16T15:14:22Z","timestamp":1539702862000},"page":"619-648","source":"Crossref","is-referenced-by-count":2,"title":["Nilpotency and strong nilpotency for finite semigroups"],"prefix":"10.1093","volume":"70","author":[{"given":"J","family":"Almeida","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica e Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre, 687, Porto, Portugal"}]},{"given":"M H","family":"Shahzamanian","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica e Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre, 687, Porto, Portugal"}]},{"given":"M","family":"Kufleitner","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Loughborough University, Epinal Way, Loughborough, Leicestershire, UK"}]}],"member":"286","published-online":{"date-parts":[[2018,11,21]]},"reference":[{"key":"2019071604364420200_hay059C1","first-page":"xvi+359","article-title":"Algebraic theory of machines, languages, and semigroups","volume-title":"Arbib","author":"Arbib","year":"1968"},{"key":"2019071604364420200_hay059C2","author":"Almeida"},{"key":"2019071604364420200_hay059C3","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1142\/9789812776884_0009","volume-title":"Semigroups, Algorithms, Automata and Languages (Coimbra, 2001)","author":"Almeida","year":"2002"},{"key":"2019071604364420200_hay059C4","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1090\/S0002-9947-01-02857-4","article-title":"Dynamics of implicit operations and tameness of pseudovarieties of groups","volume":"354","author":"Almeida","year":"2002","journal-title":"Trans. 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