arXiv · 1301.2171
A finite interval in the subsemigroup lattice of the full transformation monoid
Abstract
In this paper we describe a portion of the subsemigroup lattice of the \emph{full transformation semigroup} $Ω^Ω$, which consists of all mappings on the countable infinite set $Ω$. Gavrilov showed that there are five maximal subsemigroups of $Ω^Ω$ containing the symmetric group $\sym(Ω)$. The portion of the subsemigroup lattice of $Ω^Ω$ which we describe is that between the intersection of these five maximal subsemigroups and $Ω^Ω$. We prove that there are only 38 subsemigroups in this interval, in contrast to the $2^{2^{\aleph_0}}$ subsemigroups between $\sym(Ω)$ and $Ω^Ω$.
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Julius Jonušas, J. D. Mitchell. 2013-08-02. A finite interval in the subsemigroup lattice of the full transformation monoid. https://arxiv.org/abs/1301.2171
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