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 | References | Similar Articles | Additional Information

Abstract: To solve two problems of Bergman stated in 1981, we construct a group such that contains a free noncyclic subgroup (hence, satisfies no group identity) and , 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:
https://doi.org/10.1090/S0002-9939-05-07903-7

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.