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Some Contributions to the Theory of Transformation Monoids

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Some Contributions to the Theory of Transformation Monoids

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Ballester-Bolinches, Adolfo; Cosme i Llópez, Enric; Jiménez-Seral, P.

Aquest document és un/a article, creat/da en: 2019

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.

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