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On approximation of locally compact groups by finite algebraic systems
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## On approximation of locally compact groups by finite algebraic systems

### L. Yu. Glebsky and Peter E. I. Gordon

**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 $G$ 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.

*Copyright 2004 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**10** (2004), pp. 21-28
- Publisher Identifier: S 1079-6762(04)00126-X
- 2000
*Mathematics Subject Classification*. Primary 26E35, 03H05; Secondary 28E05, 42A38
*Key words and phrases*. Approximation, group, quasigroup
- Received by editors June 16, 2003
- Posted on March 30, 2004
- Communicated by Efim Zelmanov
- Comments (When Available)

**L. Yu. Glebsky**

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

*E-mail address:* `glebsky@cactus.iico.uaslp.mx`

**E. I. Gordon**

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

*E-mail address:* `cfyig@eiu.edu`

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

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