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Keywords = maximal centralising monoid

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Article
Centralising Monoids with Low-Arity Witnesses on a Four-Element Set
by Mike Behrisch and Edith Vargas-García
Symmetry 2021, 13(8), 1471; https://doi.org/10.3390/sym13081471 - 11 Aug 2021
Cited by 3 | Viewed by 2121
Abstract
As part of a project to identify all maximal centralising monoids on a four-element set, we determine all centralising monoids witnessed by unary or by idempotent binary operations on a four-element set. Moreover, we show that every centralising monoid on a set with [...] Read more.
As part of a project to identify all maximal centralising monoids on a four-element set, we determine all centralising monoids witnessed by unary or by idempotent binary operations on a four-element set. Moreover, we show that every centralising monoid on a set with at least four elements witnessed by the Mal’cev operation of a Boolean group operation is always a maximal centralising monoid, i.e., a co-atom below the full transformation monoid. On the other hand, we also prove that centralising monoids witnessed by certain types of permutations or retractive operations can never be maximal. Full article
(This article belongs to the Special Issue The Study of Lattice Theory and Universal Algebra)
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