In the mathematical area of group theory, the Grigorchuk group or the first Grigorchuk group is a finitely generated group constructed by Rostislav Grigorchuk that provided the first example of a finitely generated group of intermediate (that is, faster than polynomial but slower than exponential) growth. The group was originally constructed by Grigorchuk in a 1980 paper[1] and he then proved in a 1984 paper[2] that this group has intermediate growth, thus providing an answer to an important open problem posed by John Milnor in 1968. The Grigorchuk group remains a key object of study in geometric group theory, particularly in the study of the so-called branch groups and automata groups, and it has important connections with the theory of iterated monodromy groups.[3]
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^Volodymyr Nekrashevych. Self-similar groups. Mathematical Surveys and Monographs, 117. American Mathematical Society, Providence, RI, 2005. ISBN 0-8218-3831-8.
mathematical area of group theory, the Grigorchukgroup or the first Grigorchukgroup is a finitely generated group constructed by Rostislav Grigorchuk that provided...
University. Grigorchuk is particularly well known for having constructed, in a 1984 paper, the first example of a finitely generated group of intermediate...
Certain groups of birational transformations of algebraic surfaces. Examples of groups not satisfying the Tits alternative are: the Grigorchukgroup; Thompson's...
lattices in semisimple Lie groups. Wallpaper groups Baumslag–Solitar groups Fundamental groups of graphs of groupsGrigorchukgroup The ping-pong lemma, a...
Hryhorchuk Rostislav Grigorchuk All pages with titles containing Hryhorchuk All pages with titles containing GrigorchukGrigorchukgroup This page lists people...
periodic groups were constructed by Golod, based on joint work with Shafarevich (see Golod–Shafarevich theorem), and by Aleshin and Grigorchuk using automata...
alternative mentioned above, groups of intermediate growth such as Grigorchuk'sgroup are not linear. Again by the Tits alternative, as mentioned above...
Grigorchuk (1953), mathematician. See Grigorchukgroup. Vladimir Drinfeld (1954), mathematician. Awarded the Fields Medal in 1990. See Quantum group,...
also locally quasiconvex word-hyperbolic groups and therefore have the Howson property. The Grigorchukgroup G of intermediate growth does not have the...
presentation has been fruitful in fields such as algebraically closed groups and the Grigorchuk topology. In the literature, in a context where absolute presentations...
груповому етапі Ліги чемпіонів”. sport.if.ua. 27 June 2022 "Ventspils end Grigorchuk era". 11 August 2009. Archived from the original on 22 February 2014....
finitely generated torsion groups were constructed by Aleshin, Olshanskii, and Grigorchuk, using automata. Consequently, free groups of rank at least two are...
Professor of Moscow State University. His doctoral students include Rostislav Grigorchuk and Yiangdong Ye. On 7 November 2020, Stepin died at the age of 80. Kolmogorov...
relatively hyperbolic groups. Grigorchuk and Ivanov explored several natural generalizations of Dehn function for group presentations on finitely many...
Society. ISBN 9780821834725. Lewis Bowen; R. I. Grigorchuk; Yaroslav Vorobets (2012). Dynamical Systems and Group Actions. American Mathematical Society. ISBN 9780821869222...
Amer. Math. Soc. (N.S.). 40: 247–252. doi:10.1090/s0273-0979-03-00978-9. Grigorchuk, Rostislav I. (2004). "Review of Subgroup growth by Alexander Lubotzky...
Gillet Shafi Goldwasser Thomas G. Goodwillie Cameron Gordon Rostislav Grigorchuk Karsten Grove Günter Harder Ami Harten Helmut Hofer Philip Holmes Annick...
Mathematics 56 (2003), no. 7, 839–873. doi:10.1002/cpa.10076 with Rostislav Grigorchuk, Peter Linnell, Andrzej Żuk: On a question of Atiyah. Comptes rendus de...
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