On identities in groups of fractions of cancellative semigroups
classification
🧮 math.GR
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groupidentitysatisfiesbergmancancellativeconstructcontainsfractions
read the original abstract
To solve two problems of Bergman stated in 1981, we construct a group $G$ such that $G$ contains a free noncyclic subgroup (hence, $G$ satisfies no group identity) and $G$, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity.
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