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On identities in groups of fractions of cancellative semigroups

S. V. Ivanov·A. M. Storozhev
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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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S. V. Ivanov, A. M. Storozhev. 2003-12-29. On identities in groups of fractions of cancellative semigroups. https://arxiv.org/abs/math/0312493

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