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
DOI:
https://doi.org/10.1090/S1079-6762-04-00126-X
Published electronically:
March 30, 2004
MathSciNet review:
2048428
Full-text PDF Free Access
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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 $G$ 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.
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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
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
