Based among others on examples of W. M. Kantor and A. Lubotzky, L. Pyber has asked whether every finitely generated profinite group which is not PFG admits an infinite epimorphic image which is PFG. We show that the answer is negative, by constructing a 2-generated profinite group which is not PFG, and all of whose proper epimorphic images are finite.
A 2-generated just-infinite profinite group which is not positively generated.
LUCCHINI, ANDREA
2004
Abstract
Based among others on examples of W. M. Kantor and A. Lubotzky, L. Pyber has asked whether every finitely generated profinite group which is not PFG admits an infinite epimorphic image which is PFG. We show that the answer is negative, by constructing a 2-generated profinite group which is not PFG, and all of whose proper epimorphic images are finite.
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