Block-groups and Hall relations

Azza M. Gaysin; Mikhail V. Volkov

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arXiv · 2009.05627

Block-groups and Hall relations

Azza M. Gaysin·Mikhail V. Volkov

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Abstract

A binary relation on a finite set is called a Hall relation if it contains a permutation of the set. Under the usual relational product, Hall relations form a semigroup which is known to be a block-group, that is, a semigroup with at most one idempotent in each $\mathrsfs{R}$-class and each $\mathrsfs{L}$-class. Here we show that in a certain sense, the converse is true: every block-group divides a semigroup of Hall relations on a finite set.

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Azza M. Gaysin, Mikhail V. Volkov. 2020-09-11. Block-groups and Hall relations. https://arxiv.org/abs/2009.05627

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