Elementary classes of groups

Mathematical Notes

Volumn 72, Issue 1-2, 2002, Pages 75-82

  Osin, D V ^a  

^a Ministry of Finances of the Russian Federation   (Russian Federation)

Author keywords

Elementary amenable groups; Elementary classes of groups; Group growth; Kurosh Chernikov classes of groups

Indexed keywords

EID: 0141513962     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019869105364     Document Type: Article

References (13)

1. J. von Neumann, "Zur allgemeinen Theorie des Masses," Fund. Math., 13 (1929), 73-116.
2. M. M. Day, "Amenable semigroups," Illinois J. Math., 1 (1957), 509-544.
3. Ch. Chou, "Elementary amenable groups," Illinois J. Math., 24 (1980), 396-407.
4. S. N. Chernikov and A. G. Kurosh, "Solvable and nilpotent groups," Uspekhi Mat. Nauk [Russian Math. Surveys], 2 (1947), 18-59.
5. Yu. P. Razmyslov, Identities of Algebras and Their Representations, vol. 138, Transl. Math. Monographs, Amer. Math. Soc, Providence, R.I., 1994.
6. A. Yu. Ol'shanskii, The Geometry of Defining Relations in Groups [in Russian], Nauka, Moscow, 1989.
7. R. I. Grigorchuk, "To the Milnor problem of group growth," Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 271 (1983), 30-33.
8. J. A. Wolf, "Growth of finitely generated solvable groups and curvature of Riemannian manifolds," J. Diff. Geom., 2 (1968), 421-446.
9. M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of Group Theory [in Russian], Nauka, Moscow, 1982.
10. R. I. Grigorchuk and J. Wilson, Rigidity Properties of Branch Groups, Preprint, University of Geneva, 2001.
11. S. Rosset, "A property of groups of non-exponential growth," Proc. Amer. Math. Soc., 54 (1976), 24-26.
12. M. Gromov, "Groups of polynomial growth and expanding maps," Publ. Math. IHES, 53 (1981), 53-73.
13. H. Neumann, Varieties of Groups, West Berlin, 1967.