Abstract
We construct a finitely generated profinite branch group which is just-infinite and not positively finitely generated.
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L. Bartholdi, A Wilson group of non-uniformly exponential growth. C. R., Math., Acad. Sci. Paris 336 (2003), 549–554.
Bhattacharjee M.: The probability of generating certain profinite groups by two elements. Isr. J. Math. 86, 311–329 (1994)
Bondarenko I.: Finite generation of iterated wreath products. Arch. Math. 95, 301–308 (2010)
E. Detomi and A. Luccini, Characterization of finitely generated infinitely iterated wreath products, Forum Math. (2011), avilable at http://arxiv.org/abs/1104.4198.
R. Grigorchuk, Just infinite branch groups, In New Horizons in pro-p Groups. Prog. Math., vol. 184, pages 121–179. Birkhäuser, Boston, 2000.
Jaikin-Zapirain A., Pyber L.: Random generation of finite and profinite groups and group enumeration. Ann. of Math. 173, 769–814 (2011)
Lucchini A.: A 2-generated just-infinite profinite group which is not positively generated. Isr. J. Math. 141, 119–123 (2004)
Mann A., Shalev A.: Simple groups, maximal subgroups, and probabilistic aspects of profinite groups. Isr. J. Math. 96, 449–468 (1996)
M. Quick, Probabilistic generation of wreath products of non-abelian finite simple groups II, Internat. J. Algebra Comput. 16 (2006), 493–503.
C. Reid, On a construction of A. Lucchini, Preprint, avilable at http://arxiv.org/abs/1106.4423, 2011.
Segal D.: The finite images of finitely generated groups. Proc. Lond. Math. Soc. 82, 597–613 (2001)
Wiegold J.: Growth sequences of finite groups III. J. Austral. Math. Soc. 25, 142–144 (1978)
Wilson J.: Groups with every proper quotient finite. Proc. Camb. Philos. Soc. 69, 373–391 (1971)
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Samoilovych, I.O. A finitely generated just-infinite profinite branch group which is not positively finitely generated. Arch. Math. 102, 219–223 (2014). https://doi.org/10.1007/s00013-013-0597-x
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DOI: https://doi.org/10.1007/s00013-013-0597-x