Presentations of groups with even length relations

Webster, Isobel

doi:10.1080/00927872.2021.1955903

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2023

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“…Therefore, the most plausible class of semigroup that presents a better analysis through presentations are the Finitely Presented Semigroup. Evidently, in some special cases much information about a particular abstract structure can be derived from a given presentation [1,2]. A classical example of this is Coxeter Presentations [3].…”

Section: Introductionmentioning

confidence: 99%

On Presentations of Semigroup of Transformations Restricted by an Equivalence

Ibrahim

Oluyori²

2023

ARJOM

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For a non-empty set X denote the full transformation semigroup of X by T(X). Let \(\sigma\) be an equivalence relation on X and E(X, \(\sigma\)) denotes the semigroup (under composition) of all \(\alpha\) : X \(\mapsto\) X, such that \(\sigma\) \(\subseteq\) ker(\(\alpha\) ). Semigroup of transformations with restricted equivalence occur when we take all transformations whose kernel is contained in some fixed equivalence, E(X, \(\sigma\)). First, we found that E(X, \(\sigma\)) is a disjoint union copies of two generating sets. Next, we discuss the presentations, acts, subacts, direct products and bilateral semidirect product of the semigroup of transformation with restricted equivalence E(X, \(\sigma\)) and its application.

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Section: Introductionmentioning

confidence: 99%