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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 $$M\,M^{-1}… Click to show full abstract
Marek Kuczma asked in 1980 whether for every positive integer n, there exists a subsemigroup M of a group G, such that G is equal to the n-fold product $$M\,M^{-1} M\,M^{-1} \ldots \,M^{(-1)^{n-1}}$$MM-1MM-1…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 a family of subsets of a group. We also sketch several variants of the latter result.
Keywords:
submonoids groups;
group;
representability restricted;
relation;
groups group;
group representability
Journal Title: Algebra universalis
Year Published: 2017
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Journal Title: Algebra universalis
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!