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.
\Bibitem{Gri84}
\by R.~I.~Grigorchuk
\paper Degrees of growth of finitely generated groups, and the theory of invariant means
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 2
\pages 259--300
\mathnet{http://mi.mathnet.ru/eng/im1503}
\crossref{https://doi.org/10.1070/IM1985v025n02ABEH001281}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=764305}
\zmath{https://zbmath.org/?q=an:0583.20023}
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https://doi.org/10.1070/IM1985v025n02ABEH001281
https://www.mathnet.ru/eng/im/v48/i5/p939
This publication is cited in the following 142 articles:
Petr Naryshkin, Spyridon Petrakos, “Almost Finiteness and Groups of Dynamical Origin”, International Mathematics Research Notices, 2025:3 (2025)
Corentin Bodart, “Rational cross‐sections, bounded generation, and orders on groups”, Journal of London Math Soc, 109:6 (2024)
V. S. Guba, “R. Thompson's group F and the amenability problem”, Russian Math. Surveys, 77:2 (2022), 251–300
Jérémie Brieussel, Thibault Godin, Bijan Mohammadi, “Numerical upper bounds on growth of automaton groups”, Int. J. Algebra Comput., 32:01 (2022), 159
Thiebout Delabie, Juhani Koivisto, François Le Maître, Romain Tessera, “Quantitative measure equivalence between amenable groups”, Annales Henri Lebesgue, 5 (2022), 1417
M. V. Zaicev, D. D. Repovš, “Colength Growth Functions of Nonassociative Algebras”, Math. Notes, 109:3 (2021), 405–412
R. I. Grigorchuk, P.-H. Leemann, T. V. Nagnibeda, “Finitely generated subgroups of branch groups and subdirect products of just infinite groups”, Izv. Math., 85:6 (2021), 1128–1145
I. A. Reshetnikov, “Kombinatorika slov, faktordinamika i normalnye formy”, Chebyshevskii sb., 22:2 (2021), 202–235
Victor Petrogradsky, “Nil restricted Lie algebras of oscillating intermediate growth”, Journal of Algebra, 588 (2021), 349
Victor Petrogradsky, Ivan Shestakov, “Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras”, Journal of Algebra, 574 (2021), 453
Denis Osin, “Condensed groups in product varieties”, Journal of Group Theory, 24:4 (2021), 753
D. Osin, “A topological zero-one law and elementary equivalence of finitely generated groups”, Annals of Pure and Applied Logic, 172:3 (2021), 102915
Ning Yang, “Automata groups generated by Cayley machines of groups of nilpotency class two”, Int. J. Algebra Comput., 31:05 (2021), 915
Rostislav Grigorchuk, Supun Samarakoon, “Integrable and Chaotic Systems Associated with Fractal Groups”, Entropy, 23:2 (2021), 237
S. T. Samarakoon, “On growth of generalized Grigorchuk's overgroups”, Algebra Discrete Math., 30:1 (2020), 97–117
Yash Lodha, “Approximating nonabelian free groups by groups of homeomorphisms of the real line”, Journal of Algebra, 563 (2020), 292
G. Yu, “The Novikov conjecture”, Russian Math. Surveys, 74:3 (2019), 525–541
V. I. Trofimov, “On Limits of Vertex-Symmetric Graphs and Their Automorphisms”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S167–S174
Lisa Clark, Ruy Exel, Enrique Pardo, Aidan Sims, Charles Starling, “Simplicity of algebras associated to non-Hausdorff groupoids”, Trans. Amer. Math. Soc., 372:5 (2019), 3669
Rostislav Grigorchuk, Dima Grigoriev, “Key agreement based on automaton groups”, Groups Complexity Cryptology, 11:2 (2019), 77
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