On identities in groups of fractions of cancellative semigroups
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- by S. V. Ivanov and A. M. Storozhev PDF
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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.References
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Additional Information
- S. V. Ivanov
- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- Email: ivanov@math.uiuc.edu
- A. M. Storozhev
- Affiliation: Australian Mathematics Trust, University of Canberra, Belconnen, ACT 2616, Australia
- Email: andreis@amt.canberra.edu.au
- Received by editor(s): November 2, 2003
- Published electronically: February 24, 2005
- Additional Notes: The first author was supported in part by NSF grants DMS 00-99612, 04-00746
- Communicated by: Jonathan I. Hall
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1873-1879
- MSC (2000): Primary 20E10, 20F05, 20F06, 20M05
- DOI: https://doi.org/10.1090/S0002-9939-05-07903-7
- MathSciNet review: 2137850