Geodesic
On approximation of locally compact groups by finite algebraic systems
Glebsky, L.1 ; Gordon, E.2
1 IICO-UASLP, Av. Karakorum 1470, Lomas 4ta Session, SanLuis Potosi SLP 78210, Mexico
2 Department of Mathematics and Computer Science, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920-3099
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 21-28 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-04-00126-X

Glebsky, L. 1 ; Gordon, E. 2

1 IICO-UASLP, Av. Karakorum 1470, Lomas 4ta Session, SanLuis Potosi SLP 78210, Mexico
2 Department of Mathematics and Computer Science, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL 61920-3099 
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Glebsky, L.; Gordon, E. On approximation of locally compact groups by finite algebraic systems. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 21-28. doi: 10.1090/S1079-6762-04-00126-X

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