The rank of the endomorphism monoid of a uniform partition

被引：0
作者：
João Araújo
Csaba Schneider
机构：
[1] Universidade Aberta,Informatics Research Laboratory
[2] Computer and Automation Research Institute,Centro de Álgebra
[3] Universidade de Lisboa,undefined
来源：
Semigroup Forum | 2009年 / 78卷
关键词：
Transformation semigroups; Rank; Relative rank; Wreath product; Symmetric groups;
D O I：
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摘要：
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.
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