On approximation of locally compact groups by finite algebraic systems

Authors:
L. Yu. Glebsky and E. I. Gordon

Journal:
Electron. Res. Announc. Amer. Math. Soc. **10** (2004), 21-28

MSC (2000):
Primary 26E35, 03H05; Secondary 28E05, 42A38

Published electronically:
March 30, 2004

MathSciNet review:
2048428

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Abstract: We discuss the approximability of locally compact groups by finite semigroups and finite quasigroups (latin squares). We show that if a locally compact group is approximable by finite semigroups, then it is approximable by finite groups, and thus many important groups are not approximable by finite semigroups. This result implies, in particular, the impossibility to simulate the field of reals in computers by finite associative rings. We show that a locally compact group is approximable by finite quasigroups iff it is unimodular.

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Additional Information

**L. Yu. Glebsky**

Affiliation:
IICO-UASLP, Av. Karakorum 1470, Lomas 4ta Session, SanLuis Potosi SLP 78210, Mexico

Email:
glebsky@cactus.iico.uaslp.mx

**E. I. Gordon**

Affiliation:
Department of Mathematics and Computer Science, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920-3099

Email:
cfyig@eiu.edu

DOI:
http://dx.doi.org/10.1090/S1079-6762-04-00126-X

Keywords:
Approximation,
group,
quasigroup

Received by editor(s):
June 16, 2003

Published electronically:
March 30, 2004

Additional Notes:
The first author was supported in part by CONACyT-NSF Grant #E120.0546 y PROMEP, PTC-62; the second author was supported in part by NSF Grant DMS-9970009

Communicated by:
Efim Zelmanov

Article copyright:
© Copyright 2004
American Mathematical Society