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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On identities in groups of fractions of cancellative semigroups


Authors: S. V. Ivanov and A. M. Storozhev
Journal: Proc. Amer. Math. Soc. 133 (2005), 1873-1879
MSC (2000): Primary 20E10, 20F05, 20F06, 20M05
Published electronically: February 24, 2005
MathSciNet review: 2137850
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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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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07903-7
PII: S 0002-9939(05)07903-7
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.