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Mat. Zametki, 2002, Volume 72, Issue 1, Pages 84–93 (Mi mz406)  

This article is cited in 11 scientific papers (total in 11 papers)

Elementary Classes of Groups

D. V. Osin

Budget and Treasury Academy, Ministry of Finance of the Russian Federation

Abstract: Let $B$ be a class of groups. The elementary class with base $B$ is defined as the minimal class of groups containing $B$ and closed with respect to taking subgroups, quotient groups, group extensions, and direct limits. Properties of such classes are studied. Some applications to the theory of elementary amenable groups and a relation to the Kurosh–Chernikov classes of generalized solvable groups are considered.

DOI: https://doi.org/10.4213/mzm406

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English version:
Mathematical Notes, 2002, 72:1, 75–82

Bibliographic databases:

UDC: 512.54
Received: 22.10.2001

Citation: D. V. Osin, “Elementary Classes of Groups”, Mat. Zametki, 72:1 (2002), 84–93; Math. Notes, 72:1 (2002), 75–82

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Osin D.V., “Algebraic entropy of elementary amenable groups”, Geom. Dedicata, 107:1 (2004), 133–151  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Navas A.S., “Several amenable groups of interval diffeomorphisms”, Bol. Soc. Mat. Mexicana, 10:2 (2004), 219–244  mathscinet  isi
    3. Navas A., “Groupes résolubles de difféomorphismes de l'intervalle, du cercle et de la droite [Solvable groups of diffeomorphisms of the interval, the circle and the real line]”, Bull. Braz. Math. Soc. (N.S.), 35:1 (2004), 13–50  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Brieussel J., “Amenability and non-uniform growth of some directed automorphism groups of a rooted tree”, Math. Z., 263:2 (2009), 265–293  crossref  mathscinet  zmath  isi  elib  scopus
    5. Gardner B.J., “Kurosh-Amitsur Radical Theory for Groups”, Analele Stiint. Univ. Ovidius C., 18:2 (2010), 73–89  mathscinet  isi
    6. Filchenkov A.A., “Mery istinnosti i veroyatnostnye graficheskie modeli dlya predstavleniya znanii s neopredelennostyu”, Trudy spiiran, 2012, no. 4, 254–295  mathnet  elib
    7. Ozawa N., Rordam M., Sato Ya., “Elementary Amenable Groups Are Quasidiagonal”, Geom. Funct. Anal., 25:1 (2015), 307–316  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Sun M.Y., “Existence of the Tracial Rokhlin Property”, J. Operat. Theor., 74:1 (2015), 3–21  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Wesolek Ph., “Elementary Totally Disconnected Locally Compact Groups”, Proc. London Math. Soc., 110:6 (2015), 1387–1434  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Erschler A., “Iterated identities and iterational depth of groups”, J. Mod. Dyn., 9 (2015), 257–284  crossref  mathscinet  zmath  isi  scopus
    11. Wesolek Ph., Williams J., “Chain Conditions, Elementary Amenable Groups, and Descriptive Set Theory”, Group. Geom. Dyn., 11:2 (2017), 649–684  crossref  mathscinet  zmath  isi  scopus  scopus
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