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The rank of the endomorphism monoid of a uniform partition
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Resumo(s)
The rank of a semigroup is the cardinality of a smallest generating set. In this paper we compute the rank of the endomorphism monoid of a non-trivial uniform partition of a finite set, that is, the semigroup of those transformations of a finite set that leave a non-trivial uniform partition invariant. That involves proving that the rank of a wreath product of two symmetric groups is two and then use the fact that the endomorphism monoid of a partition is isomorphic to a wreath product of two full transformation semigroups. The calculation of the rank of these semigroups solves an open question.
Descrição
Palavras-chave
Transformation semigroups Wreath product Symmetric groups Rank Relative rank
Contexto Educativo
Citação
Schneider, Csaba; Araújo, João - The rank of the endomorphism monoid of a uniform partition. " Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 78, nº 3 (June 2009), p. 498-510
Editora
Springer Verlag