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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