Geodesic
Residual finiteness of groups and topological dynamics
Sbornik. Mathematics, Tome 191 (2000) no. 4, pp. 529-541 
A. V. Egorov. Residual finiteness of groups and topological dynamics. Sbornik. Mathematics, Tome 191 (2000) no. 4, pp. 529-541. http://geodesic.mathdoc.fr/item/SM_2000_191_4_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The property of residual finiteness of finitely generated groups admits an interpretation in terms of topological dynamics. In this paper it is proved that a finitely generated group is residually finite if and only if it is isomorphic to a group whose action on some compact set is efficient and distal.

[1] Khyuitt E., Ross K., Abstraknyi garmonicheskii analiz, T. 1, Nauka, M., 1975

[2] Merzlyakov Yu. I., Ratsionalnye gruppy, Nauka, M., 1987 | MR | Zbl

[3] Bronshtein I. U., Rasshireniya minimalnykh grupp preobrazovanii, Shtiintsa, Kishinev, 1975 | MR

[4] Auslender L., Grin L., Khan F., Potoki na odnorodnykh prostranstvakh, Mir, M., 1966 | MR

[5] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968 | MR

[6] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR

[7] Shiryaev A. N., Veroyatnost, Nauka, M., 1989 | MR

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

[9] Ryll-Nardzewski C., “On fixed points of semigroups of endomorphisms of linear spaces”, Proc. 5th Berkeley Symp. Math. Stat. Probab., V. 2, Part 1 (Univ. Calif. 1965/66), 1967, 55–61 | MR | Zbl

[10] Edvards R., Funktsionalnyi analiz. Teoriya i prilozheniya, Mir, M., 1969