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We construct finitely generated Engel branch groups, answering a question of Fern\'andez-Alcober, Noce and Tracey on the existence of such objects.
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Laurent Bartholdi, Rostislav I. Grigorchuk, and Zoran Šuniḱ, Branch groups , Handbook of Algebra, vol. 3, Elsevier, 2003, pp. 989–1112
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Miklós Abért, Group laws and free subgroups in topological groups , Bulletin of the London Mathematical Society 37
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V. V. Bludov, An example of not Engel group generated by Engel elements , A Conference in Honor of Adalbert Bovdi’s 70th Birthday (Debrecen, Hungary), November 2005, pp. 7–8
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Volodymyr Nekrashevych, Self-Similar Groups , Mathematical Surveys and Monographs, vol. 117, American Mathematical Society, Providence, Rhode Island, August 2005
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Gunnar Traustason, Engel groups , Groups St. Andrews 2009. Vol. II. Selected Papers of the Conference, University of Bath, Bath, UK, August 1–15, 2009., Cambridge: Cambridge University Press, 2011, pp. 520–550
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John S. Wilson, The gap in the growth of residually soluble groups , Bulletin of the London Mathematical Society 43
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by same author, Milnor’s problem on the growth of groups and its consequences , pp. 705–774, Princeton University Press, December 2014
Gustavo Fernández-Alcober and Amaia Zugadi-Reizabal, GGS-groups: Order of congruence quotients and Hausdorff dimension , Transactions of the American Mathematical Society 366
2017
Later among the works it cites.
Marialaura Noce and Antonio Tortora, A note on Engel elements in the first Grigorchuk group , International Journal of Group Theory (2018), no. Online First
2018
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Gustavo A. Fernández-Alcober, Albert Garreta, and Marialaura Noce, Engel elements in some fractal groups , Monatshefte für Mathematik 189
2019
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Gustavo A. Fernández-Alcober, Marialaura Noce, and Gareth M. Tracey, Engel elements in weakly branch groups , Journal of Algebra 554
2020
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Antonio Tortora and Maria Tota, Engel groups in bath - ten years later , International Journal of Group Theory 9
2020
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2014
Cited alongside, same era.
Anna Erschler, Iterated identities and iterational depth of groups , Journal of Modern Dynamics 9
2015
Cited alongside, same era.
Laurent Bartholdi, Algorithmic Decidability of Engel’s Property for Automaton Groups , Computer Science – Theory and Applications (Alexander S. Kulikov and Gerhard J. Woeginger, eds.), vol. 9691, Springer International Publishing, Cham, 2016, pp. 29–40
2016
Cited alongside, same era.
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Steffen Kionke and Eduard Schesler, Realizing residually finite groups as subgroups of branch groups , December 2022
2022
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J. Moritz Petschick, Two periodicity conditions for spinal groups , Journal of Algebra 633
2023
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