Some contributions to the theory of transformation monoids
| Autor: | Enric Cosme-Llópez, Adolfo Ballester-Bolinches, P. Jiménez-Seral |
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| Rok vydání: | 2019 |
| Předmět: |
Classical theory
Transitive relation Pure mathematics Algebra and Number Theory Conjecture Algebraic structure 010102 general mathematics Permutation group 01 natural sciences Transformation (music) Development (topology) Mathematics::Category Theory 0103 physical sciences Àlgebra 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Ballester-Bolinches, Adolfo Cosme i Llópez, Enric Jiménez-Seral, P. 2019 Some Contributions to the Theory of Transformation Monoids Journal of Algebra 522 31 60 RODERIC. Repositorio Institucional de la Universitat de Valéncia instname |
| ISSN: | 0021-8693 |
| Popis: | The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg [A theory of transformation monoids: combinatorics and representation theory. Electron. J. Combin. 17 (2010), no. 1, Research Paper 164, 56 pp] have been answered. Our results can also be considered as a further development in the hunt for a solution of the Černý conjecture. |
| Databáze: | OpenAIRE |
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