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arXiv · 1702.06088

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

George M. Bergman
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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.

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BibTeXRIS

George M. Bergman. 2017-02-20. Submonoids of groups, and group-representability of restricted relation algebras. https://doi.org/10.1007/s00012-018-0488-x

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