2018/01/09 by Strebel, Ralph
#20E07 #20E26 #FOS: Mathematics #Group Theory (math.GR) #Primary 20E07 #Secondary: 20F05
paper · doi:10.48550/arxiv.1801.03078
In "Subgroups of free profinite groups and large subfields of Q" (Israel J. Math. 39 (1981), no. 1-2, pages 25-45; MR 617288) A. Lubotzky and L. van den Dries raise the question whether a finitely generated, residually finite group is necessarily free if the rank function on its subgroups of finite index satisfies Schreier's well-known index rank relation (see Question 2 on p. 34). I answered this question in 1980 but, so far, I have not published my answer. This note fills the omission; it gives an amended and abridged version of my original proof.