On identities in groups of fractions of cancellative semigroups
S. V. Ivanov, A. M. Storozhev
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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