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arXiv · 1801.03078

A converse to Schreier's index-rank formula

Ralph Strebel
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Abstract

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.

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Ralph Strebel. 2018-01-09. A converse to Schreier's index-rank formula. https://arxiv.org/abs/1801.03078

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