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Commutative nilpotent transformation semigroups
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Orientador(es)
Resumo(s)
Cameron et al. determined the maximum size of a null subsemigroup of the full transformation semigroup T(X) on a finite set X and provided a description of the null semigroups that achieve that size. In this paper we extend the results on null semigroups (which are commutative) to commutative nilpotent semigroups. Using a mixture of algebraic and combinatorial techniques, we show that, when X is finite, the maximum order of a commutative nilpotent subsemigroup of T(X) is equal to the maximum order of a null subsemigroup of T(X) and we prove that the largest commutative nilpotent subsemigroups of T(X) are the null semigroups previously characterized by Cameron et al.
Descrição
Funding Information: This work is funded by national funds through the FCT\u2014Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The third author is funded by national funds through the FCT\u2014Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia, I.P., under the scope of the studentship 2021.07002.BD. We thank the referee for their careful reading of the paper and their many helpful comments and suggestions. The authors are also thankful to Ricardo P. Guilherme for his helpful comments. Publisher Copyright: © The Author(s) 2024.
Palavras-chave
Algebra and Number Theory