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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 5, Pages 939–985 (Mi izv1503)  

This article is cited in 89 scientific papers (total in 89 papers)

Degrees of growth of finitely generated groups, and the theory of invariant means

R. I. Grigorchuk


Abstract: This paper gives a negative solution to the problem of Milnor concerning the degrees of growth of groups. The construction also answers a question of Day concerning amenable groups. A number of other results are obtained on residually finite finitely generated infinite 2-groups.
Bibliography: 51 titles.

Full text: PDF file (4654 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:2, 259–300

Bibliographic databases:

UDC: 512
MSC: 20F05
Received: 27.05.1983

Citation: R. I. Grigorchuk, “Degrees of growth of finitely generated groups, and the theory of invariant means”, Izv. Akad. Nauk SSSR Ser. Mat., 48:5 (1984), 939–985; Math. USSR-Izv., 25:2 (1985), 259–300

Citation in format AMSBIB
\Bibitem{Gri84}
\by R.~I.~Grigorchuk
\paper Degrees of growth of finitely generated groups, and the theory of invariant means
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 5
\pages 939--985
\mathnet{http://mi.mathnet.ru/izv1503}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=764305}
\zmath{https://zbmath.org/?q=an:0583.20023}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 2
\pages 259--300
\crossref{https://doi.org/10.1070/IM1985v025n02ABEH001281}


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    This publication is cited in the following articles:
    1. R. I. Grigorchuk, “On the growth degrees of $p$-groups and torsion-free groups”, Math. USSR-Sb., 54:1 (1986), 185–205  mathnet  crossref  mathscinet  zmath
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    4. R. I. Grigorchuk, “On the Hilbert–Poincaré series of graded algebras associated with groups”, Math. USSR-Sb., 66:1 (1990), 211–229  mathnet  crossref  mathscinet  zmath  isi
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    6. Norbert Seifter, “Properties of graphs with polynomial growth”, Journal of Combinatorial Theory, Series B, 52:2 (1991), 222  crossref  mathscinet  zmath  isi
    7. Max Garzon, Yechezkel Zalcstein, “The complexity of Grigorchuk groups with application to cryptography”, Theoretical Computer Science, 88:1 (1991), 83  crossref  mathscinet  zmath  isi
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    22. R. I. Grigorchuk, V. V. Nekrashevych, “The group of asynchronous automata and rational homeomorphisms of the Cantor set”, Math. Notes, 67:5 (2000), 577–581  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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