The Rank of the Endomorphism Monoid of a Partition

Simple item page
dc.creatorAraujo, Joao
dc.creatorSchneider, Csaba
dc.date2008-07-08
dc.date.accessioned2026-07-07T09:49:04Z
dc.date.available2026-07-07T09:49:04Z
dc.descriptionThe 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.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0807.1214
dc.identifierhttp://arxiv.org/abs/0807.1214
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164446
dc.subjectGroup Theory
dc.subjectRings and Algebras
dc.subject20M20, 20B30, 20E22
dc.titleThe Rank of the Endomorphism Monoid of a Partition
dc.typetext

Files

Collections

arXiv