Abstract
We construct a 2-generated profinite group which is just-infinite and not positively generated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Bhattacharjee,The probability of generating certain profinite groups by two elements, Israel Journal of Mathematics86 (1994), 311–329. MR95c:20039.
A. V. Borovik, L. Pyber and A. Shalev,Maximal subgroups in finite and profinite groups, Transactions of the American Mathematical Society348 (1996), 3745–3761. MR96m:20046.
F. Dalla Volta, A. L. and F. Morini,On the probability of generating a minimal d-generated group, Journal of the Australian Mathematical Society71 (2001), no. 2, 177–185, Special issue on Group Theory. MR2002f:20121.
F. Dalla Volta and A. Lucchini,Finite groups that need more generators than any proper quotient, Journal of the Australian Mathematical Society. Series A64 (1998), 82–91. MR99a:20030.
W. M. Kantor and A. Lubotzky,The probability of generating a finite classical group, Geometriae Dedicata36 (1990), 67–87. MR91j:20041.
A. Mann,Positively finitely generated groups, Forum Mathematicum8 (1996), 429–459. MR97j:20029.
A. Mann and A. Shalev,Simple groups, maximal subgroups, and probabilistic aspects of profinite groups, Israel Journal of Mathematics96 (1996), 449–468.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper was mainly conceived during the workshop “Groups and Probability” organized in Budapest (June 30 – July 4, 2003) by the Erdős Center. Stimulating conversations during the conference led to this result and the author is grateful to both the organizers and the participants.
Rights and permissions
About this article
Cite this article
Lucchini, A. A 2-generated just-infinite profinite group which is not positively generated. Isr. J. Math. 141, 119–123 (2004). https://doi.org/10.1007/BF02772214
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02772214