Geodesic
On approximation of amenable groups by finite quasigroups
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 48-58 
L. Yu. Glebskii; E. I. Gordon. On approximation of amenable groups by finite quasigroups. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 48-58. http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a4/
@article{ZNSL_2005_326_a4,
     author = {L. Yu. Glebskii and E. I. Gordon},
     title = {On approximation of amenable groups by finite quasigroups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {48--58},
     year = {2005},
     volume = {326},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a4/}
}
TY  - JOUR
AU  - L. Yu. Glebskii
AU  - E. I. Gordon
TI  - On approximation of amenable groups by finite quasigroups
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 48
EP  - 58
VL  - 326
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a4/
LA  - ru
ID  - ZNSL_2005_326_a4
ER  - 
%0 Journal Article
%A L. Yu. Glebskii
%A E. I. Gordon
%T On approximation of amenable groups by finite quasigroups
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 48-58
%V 326
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a4/
%G ru
%F ZNSL_2005_326_a4

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An amenability criterion for groups in terms of their approximation by finite quasigroups is given.

[1] M. A. Alekseev, L. Yu. Glebskii, E. I. Gordon, “Ob approksimatsiyakh grupp, gruppovykh deistvii i algebr Khopfa”, Zap. nauchn. semin. POMI, 256, 1999, 224–262 | MR | Zbl

[2] A. M. Vershik, “Schetnye gruppy, blizkie k konechnym”, Invariantnye srednie na topologicheskikh gruppakh, Mir, M., 1973, 112–135

[3] A. M. Vershik, “Amenability and approximation of infinite groups”, Sel. Math. Sov., 2:4 (1982), 311–330 | MR | Zbl

[4] A. M. Vershik, E. I. Gordon, “Gruppy, lokalno vlozhimye v klass konechnykh grupp”, Algebra i Analiz, 9:1 (1997), 71–97 | MR | Zbl

[5] L. Yu. Glebsky, E. I. Gordon, “On approximation of locally compact groups by finite algebraic systems”, Electron. Res. Announc. Amer. Math. Soc., 10 (2004), 21–28 | DOI | MR | Zbl

[6] L. Yu. Glebsky, E. I. Gordon, “On approximation of locally compact groups by finite quasigroups and finite semigroups”, Illinois Journal of Mathematics, Accepted

[7] L. Yu. Glebsky, E. I. Gordon, “On approximation of unimodular groups by finite quasigroups”, Illinois Journal of Mathematics, Accepted

[8] F. Grinlif, Invariantnye srednie na topologicheskikh gruppakh, Mir, M., 1973

[9] M. Ziman, “Extensions of Latin subsquares and local embeddability of groups and group algebras”, Quasigroups and Related Systems, 11 (2004), 115–125 | MR | Zbl

[10] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR

[11] D. Ornstein, B. Weiss, “Entropy and isomorphism theorems for actions of amenable groups”, J. d'Analyse Math., 48 (1987), 1–141 | DOI | MR | Zbl

[12] J. M. Rosenblatt, “A generalization of Fölner condition”, Math. Scand., 33 (1973), 153–170 | MR | Zbl

[13] H. J. Ryser, Combinatorial Mathematics, The Carus Mathematical Monographs, 15, 1963 | MR | Zbl

[14] A. M. Stepin, “Approksimiruemost grupp i gruppovykh deistvii”, Uspekhi mat. nauk, 38:6 (1983), 123–124 | MR | Zbl

[15] A. M. Stepin, “Approximation of groups and group actions”, Cayley topology. Ergodic theory of ${\mathbf Z}^d$-actions, London Math. Soc., Lect. Notes Series, 228, Cambridge Univ. Press, 1996, 474–484 | MR