Abstract
In this paper we describe a portion of the subsemigroup lattice of the full transformation semigroup Omega (Omega) , which consists of all mappings on the countable infinite set Omega. Gavrilov showed that there are five maximal subsemigroups of Omega (Omega) containing the symmetric group . The portion of the subsemigroup lattice of Omega (Omega) which we describe is that between the intersection of these five maximal subsemigroups and Omega (Omega) . We prove that there are only 38 subsemigroups in this interval, in contrast to the subsemigroups between and Omega (Omega) .
| Original language | English |
|---|---|
| Pages (from-to) | 183-198 |
| Number of pages | 16 |
| Journal | Semigroup Forum |
| Volume | 89 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Aug 2014 |
Keywords
- Transformation semigroups
- Maximal subsemigroups
- Lattice of subsemigroups
- CLONES
- SETS