Submonoids of groups, and group-representability of restricted relation algebras

DOI10.1007/S00012-018-0488-XarXiv1702.06088MaRDI QIDQ6283404

George M. Bergman

Publication date: 20 February 2017

Abstract: Marek Kuczma asked in 1980 whether for every positive integer $n,$ there exists a subsemigroup $M$ of a group $G,$ such that $G$ is equal to the $n$-fold product $M,M^{-1}M,M^{-1}dots,M^{(-1{)}^{n-1}},$ but not to any proper initial subproduct of this product. We answer his question affirmatively, and prove a more general result on representing a certain sort of relation algebra by subsets of a group. We also sketch several variants of the latter result.

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Cylindric and polyadic algebras; relation algebras (03G15)

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