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Nilpotency and strong nilpotency for finite semigroups

Preprint

<p>Nilpotent semigroups in the sense of Mal\textquoterightcev are defined by<br /> semigroup identities. Finite nilpotent semigroups constitute a<br /> pseudovariety, MN, which has finite rank. The semigroup<br /> identities that define nilpotent semigroups, lead us to define<br /> strongly Mal\textquoterightcev nilpotent semigroups. Finite strongly Mal\textquoterightcev<br /> nilpotent semigroups constitute a non-finite rank pseudovariety,<br /> SMN. The pseudovariety SMN is strictly contained in the<br /> pseudovariety MN but all finite nilpotent groups are in SMN. We<br /> show that the pseudovariety MN is the intersection of the<br /> pseudovariety BGnil with a pseudovariety defined by a k-identity.<br /> \%Define and study finite strongly Mal\textquoterightcev nilpotent semigroups<br /> which they were defined by inspiration from the semigroup<br /> identities that define nilpotent semigroups in the sense of<br /> Mal\textquoterightcev. We further compare the pseudovarieties MN\&nbsp;and<br /> SMN with the Mal\textquoterightcev product of the pseudovarieties J and Gnil.</p>

M. Kufleitner

M.H. Shahzamanian

Publication

Year of publication: 2017

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