Block-groups and Hall relations

2020/09/11 by Gaysin, Azza M., Volkov, Mikhail V.
#20M20 20M30 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2009.05627

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 \mathrsfsR-class and each \mathrsfsL-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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• Philip Hall's Problem On Non-Abelian Splitters